Chapter VII: Part 7

A B C D E E D C B A
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 91 | 2 | 3 | 97 | 6 | 95 | 94 | 8 | 9 | 100 |
| | | | | | | | | | | 1
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 20 | 82 | 83 | 17 | 16 | 15 | 14 | 88 | 89 | 81 |
| | | | | | | | | | | 2
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 21 | 72 | 73 | 74 | 25 | 26 | 27 | 78 | 79 | 30 |
| | | | | | | | | | | 3
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 60 | 39 | 38 | 64 | 66 | 65 | 67 | 33 | 32 | 41 |
| | | | | | | | | | | 4
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 50 | 49 | 48 | 57 | 55 | 56 | 54 | 43 | 42 | 51 |
| | | | | | | | | | | 5
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 61 | 59 | 58 | 47 | 45 | 46 | 44 | 53 | 52 | 40 |
| | | | | | | | | | | 5
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 31 | 69 | 68 | 34 | 35 | 36 | 37 | 63 | 62 | 70 |
| | | | | | | | | | | 4
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 80 | 22 | 23 | 24 | 75 | 76 | 77 | 28 | 29 | 71 |
| | | | | | | | | | | 3
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 90 | 12 | 13 | 87 | 86 | 85 | 84 | 18 | 19 | 11 |
| | | | | | | | | | | 2
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 1 | 99 | 98 | 4 | 96 | 5 | 7 | 93 | 92 | 10 |
| | | | | | | | | | | 1
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+

Fig. 7.--Plan of the Magic Hundred.]

THE TWENTY-FOUR MONKS.

During the middle ages there existed a monastery, in which lived twenty-four monks, presided over by a blind abbot. The cells of the monastery were planned as shown in the accompanying figure (Fig. 8), passages being arranged along two sides of each of the outer cells and all round the inner cell, in which the abbot took up his quarters. Three monks were allotted to each cell, making, of course, nine monks in each row of cells. The abbot, being lazy as well as blind, was very remiss in making his rounds, but provided he could count nine heads on each side of the monastery he retired into his own cloister, contented and satisfied that the monks were all within the building, and that no outsiders were keeping them company. The monks, however, taking advantage of their abbot's blindness and remissness, conspired to deceive him, a portion of their number sometimes going out and at other times receiving friends in their cells. They accomplished their deception, and it never happened that strangers were admitted when monks were out, yet there never were more nor less than nine persons upon each side of the building. Their first deception consisted in four of their number going out, upon which four monks took possession of each of the cells numbered 1, 3, 6, and 8, one monk only being left in each of the other cells; nine monks being thus on each side of the building. Upon returning, the four monks brought in four friends, when it was necessary to arrange the twenty-eight persons, two in each of the cells 1, 3, 6, and 8, and five in each of the others; still nine heads only were to be counted in either row. Emboldened by success, eight outsiders were introduced, and the thirty-two persons now were arranged one only in each of the cells 1, 3, 6, and 8, but seven in each of the other cells; again, according to the abbot's system of counting, all was well. In the next endeavour, the strangers all went away and took six monks with them, leaving but eighteen at home to represent twenty-four; these eighteen placed themselves five in each of the cells 1 and 8 and four in each of the cells 3 and 6; the remaining cells were empty, but the cells on each side of the building still contained nine monks. On returning, the six truants each brought two friends to pass the night, and the thirty-six retired to rest, nine in each of the cells 2, 4, 5, and 7; the remainder were empty, and the abbot was quite satisfied that the monks were alone in the monastery.

+-----++------++-----+
| || || |
| 1 || 2 || 3 |
| || || |
+=====++======++=====+
| || || |
| 4 ||ABBOTT|| 5 |
| || || |
+=====++======++=====+
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| 6 || 7 || 8 |
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+-----++------++-----+

Fig. 8.--The Twenty-four Monks.]

TO TAKE ONE FROM NINETEEN, SO THAT THE REMAINDER SHALL BE TWENTY.

See how it is done: XIX. (nineteen), by taking away the one that stands between the two tens (XX.), twenty will remain.

A similar catch is to write down nine figures, the sum of which is 45, from that number to take away 50, and to let the remainder be fifteen. The numerals should be added together thus: 1+2+3+4+5+6+7+8+9=45, or XLV., from which take away L. (50), and there will be left XV. (15).

THE FAMOUS FORTY-FIVE.

The number 45 can be divided into four such parts that if to the first 2 is added, from the second 2 is subtracted, the third is multiplied by 2, and the fourth divided by 2:--the total of the addition, the remainder of the subtraction, the product of the multiplication, and the quotient of the division will be the same.

The first part is 8, to which add 2, and the total will be 10
The second is 12, from which subtract 2, and the total will be 10
The third is 5, which multiply by 2, and the result will be 10
The fourth is 20, which divide by 2, and the result will be 10
--
45

Again, 45 may be subtracted from 45 in such a manner as to leave 45 for a remainder. Arrange the following figures, add the rows together, and each row will be 45; subtract the bottom row from the top row, and the sum of the result added together will also be 45.

9+8+7+6+5+4+3+2+1=45
1+2+3+4+5+6+7+8+9=45
--------------------
8+6+4+1+9+7+5+3+2=45

THE COSTERMONGER'S PUZZLE.

A costermonger bought 120 oranges at two for a penny, and 120 more at three for a penny, and mixed the oranges all together in a basket. He sold them out, hoping to receive back his money again, at the rate of five for twopence; but on counting his money he found that he had sold the oranges for fourpence less than they had cost him. How this happened will be seen by following the accompanying figures. The first forty purchasers of the oranges would take 200 out of the 240 oranges, and taking it for granted that the fruit was equally mixed, would receive for their money 100 of the oranges originally bought at two a penny and 100 of those at three a penny, and would pay for them the sum of 6s. 8d. The forty remaining oranges would bring in, at the same rate, 1s. 4d. only, making 8s. in all. The cost of the fruit was, for the first 120, 5s., and for the second 120, 3s. 4d., or 8s. 4d. in all, making the loss of 4d. on the lot. To more fully explain the matter, we will suppose the oranges not mixed, but standing in separate baskets, from which, for each purchaser, the costermonger takes two of the two a penny oranges and three of the three a penny oranges, disposing of them in that way for twopence; it will then be clearly seen that the basket containing the three a penny oranges will be first exhausted, for the first forty purchasers, each having three oranges from one basket, will take all the 120 oranges purchased at three a penny, but will require only 80 oranges from the other basket, thus leaving 40 of the two a penny oranges to be sold at five for twopence, or a loss of fourpence on the last 40 sold.

THE PROGRESSION OF NUMBERS.

An illustration of the progression of numbers may be gathered from the description given of the American puzzle of "15," at the commencement of this section on _Arithmetical Amusements_. It is there stated that the different number of combinations or different arrangements of the fifteen cubes that can be made are 1,307,674,318,000. The reader may prove this for himself in the following manner:--The number of combinations that can be made with two cubes is 2, of three cubes 6, of four cubes 24, of five cubes 120, of six cubes 720, and so on, multiplying the result each time by one number higher than the previous result was multiplied by, until the amazing total quoted is reached; the arrangement of the cubes in rows and columns introducing additional variations of combinations. There are numerous instances on record in which it is stated that advantage has been taken of the known progression that ensues upon a repeated doubling of a given result. The _Horse-dealer's Bargain_ is frequently quoted. A horse-dealer having a horse to dispose of, to which a gentleman had taken a great fancy, was asked to name any price he thought fit. Wishing at the first blush to appear generous, he offered to sell his horse, calculating its price according to the number of nails that were used to fasten on the four shoes, a farthing being allowed for the first nail, a halfpenny for the second, a penny for the third, twopence for the fourth, and so on. Upon examination it was found that it took six nails to fasten on each of the shoes, making in all twenty-four nails. The amount arrived at by repeatedly doubling the amount until the twenty-fourth nail had been allowed for was £8,738 2s. 8d.

The story of the _Sovereign and the Sage_ gives a still more wonderful result. A king once, anxious to reward one of his subjects for valuable services performed to the State, asked in what way the subject would take his recompense. The king and the subject were both sixty-four years of age, and the wise man asked that he might be granted a kernel of wheat for the first year of their lives, two for the second, four for the third, eight for the fourth, sixteen for the fifth, and so on. By continuing the calculation until the result has been doubled for the sixty-fourth time, the astounding number of 9,223,372,036,854,775,808 will appear. It is generally conceded that the average number of wheat kernels in a pint is 9,216, which will give 18,432 for a quart, 73,728 for a peck, and 589,824 for a bushel, or 31,274,997,411,298 bushels of grain as the courtier's reward for his services, a larger amount than the whole world would produce in several years.

_The Pin in the Hold of the "Great Eastern" Steamship_ is comparatively a modern calculation, based on this principle. It is calculated that 200 pins go to the ounce, and that if for the fifty-two weeks in the year one pin were dropped into the hold during the first week, two in the second, four in the third, and so on, that by the end of the year the weight of the whole would be no less than 628,292,358 tons of pins. As the _Great Eastern_ steamship was built to carry 22,500 tons only, it follows that to carry all the pins there would be required 27,924 ships of the size of the _Great Eastern_.

As a last illustration of this subject we will instance the feat of counting a billion, which all boys know is a million millions. Allowing that so many as 200, which is an outside number, could be counted in a minute, it would, excluding the 366th day in leap years, take one person upwards of 9,512 years before the task would be completed. It is not, therefore, probable that any one person has yet counted a billion.

We next proceed to give a few of the rules showing

HOW A NUMBER THOUGHT OF OR OTHERWISE INDICATED MAY BE TOLD.

These rules and puzzles are numerous, and in practising them in company it is well to have several methods at command, in order that those of the company not in the secret may be the more mystified; and, indeed, those who only know one or two ways will themselves be astonished if they see others proceeding on principles differing from those with which they are familiar.

_The Cancelled Figure._--Write down on a slate a series of numbers, the sum of each of which shall be 9: such, for example, as 18, 27, 36, 45, 144, 234, 612, 711, 252, 342, 261, 360, 432, 315, &c. &c. The greater the variety the better. Tell some person to fix on two of these numbers, and after adding them together, to strike out any one of the figures of the result, and then, upon his stating the sum of the remaining figure or figures, the figure struck out may be arrived at by ascertaining the difference between that sum and 9 or 18, according to whether the sum is less or more than 9. If the sum remaining be 9, the figure struck out will have been 9. Suppose, for instance, the numbers selected are 711 and 252, the total of which will be 963; if the figure struck out of that number be 6, the sum of the two remaining figures will be 12, or 6 less than 18. Again, take the numbers 18 and 27, making a total of 45; strike out the 5, and it will be seen that the difference between 4 and 9 is 5.

In the following methods any number may be thought of, and the subsequent calculations are to be mentally or otherwise made by him thinking of the number.

_First Method._--Instruct that the number thought of be multiplied by 3, that 1 be added to the result, the result again being multiplied by 3, to which result the number first thought of has to be added; ask the result, strike off mentally the final figure, which will be a 3, and the figure or figures then left will represent the number first thought of. For example:--

The number thought of is 11
Multiplied by 3, it is 33
Add 1 34
Multiply by 3 102
Add the number (11) thought of 113

The result of which, when told, will show 11 to be the number thought of.

_Second Method._--Let any number be thought of, which we will
again suppose to be 11
Instruct that it be doubled 22
Instruct that some stated even number be added
(say 54) 76
Let the result be halved 38
Deduct the number first thought of (11) 27

The result will always be the half of the number that was instructed to be added.

_Third Method._--Multiply the number thought of by itself
(say 11). 121
Take 1 from the number thought of, and multiply
the result by itself (10+10) 100
---
Ask the difference between the two results 21

To this number the player, who is exhibiting his powers, must mentally add 1=22, and divide that number by 2, which gives 11, the number thought of.

_Fourth Method._--Add 1 to the number thought of (again 11) 12
Multiply by 3 36
Add 1 37
Add the number thought of (11) 48

Ask the result, from which mentally subtract 4, and divide the result by 4, which will again correctly give the original number.

_Fifth Method._--Let the number (11) thought of be doubled 22
Add 4 26
Multiply by 5 130
Add 12 142
Multiply by 10 1,420

Ask the result, from which mentally deduct 320, giving 1,100, from which strike off the noughts, and the result is again as before.

_Sixth Method._--Let 1 be deducted from the number (11)
thought of 10
Multiply by 2 20
Add number first thought of 31

Ask the result, and to it mentally add 3=34, divide by 3, and the quotient of full numbers will be the number thought of. The above methods of guessing a number thought of will be about as many as any lad can remember.

MAGICAL ADDITION.

The following is a peculiar arrangement of the figures 1 to 9, so that by adding them together they amount to 100:--

15
36
47
---
98
2
---
100

_To find the sum-total of three lines of figures upon the first line being shown_, let any one write down a row of figures, and suppose they are 76854. Then take the paper, and, leaving space for two more rows of figures, say that the result of the addition of that row with two other rows can be given, the first of which rows may be written by any one present. Proceed by deducting 1 from the final right-hand figure, and place the figure 1 on the left-hand side; let the top row be folded over, and the paper handed back for the second row to be written, which we will suppose to be 34721; fill in the third row by making each figure in the second row up to 9 by writing 65278; the figures given according to the instructions will be the addition of the three rows.

76854
34721
65278
------
176853
------

_The addition of five rows of figures may be told in a similar manner._ Let any one present write down, as before, a row of figures, and then the calculator may undertake to tell the addition of that row with four other rows, two of which may be written by any person or persons present. This is attained by deducting 2 from the unit figure, and placing the figure 2 on the left-hand side. For example: again suppose the first row to be as before (76854); the result of the addition of that row and four others may be made to be 276852. After the first row has been written, fold it over, and request some one to write a second row of figures, which shall be supposed to be 34721; to this the magic calculator should write for the third row such figures as will make each of the above up to 9, namely, 65278; again, let a stranger write the fourth row, first turning over so as to conceal the second and third rows; whatever appears for the fourth row must be in each figure, as before, for the fifth row, made by the calculator to 9. Thus, if the fourth row be put down 80765, the necessary figures to add for the fifth row will be 19234, when the previously given total will be found to be correct.

76854
34721
65278
80765
19234
------
276852
------

In the last two examples of _Magical Addition_ the only stipulations needed are that no subsequent row shall contain more figures than are contained in the first row, and that the first row shall end neither with a 1 nor a 0.

THE CLEVER LAWYER.

The following good story is very old:--A country attorney was once left executor to a will in which the testator bequeathed his stable of horses to be divided among three persons, in the proportions of half of the horses to A, a third of the horses to B, and a ninth of the horses to C. When the will was made 18 horses were in the stable, but subsequently, and before the death of the testator, one died, leaving but 17. The division according to the will now seemed impossible; but to prevent disputes among the legatees, the lawyer gave a horse out of his own stable, then divided the horses according to the will, and yet received his own back, and all were satisfied. It was done in the following manner:--

A received the half of 18, namely 9 horses.
B " third " 6 "
C " ninth " 2 "
--
17
The lawyer's horse returned 1
--
18

A NEW WAY OF MULTIPLYING BY 9.

Suppose it be required to multiply the following figures by 9, the result may be obtained in the following as well as in the ordinary way. In the first example the ordinary method has been pursued; the new way consists in adding a 0 on the right-hand side of the figures, and subtracting the number to be multiplied.

467543 4675430
9 467543
------- -------
4207887 4207887

TO REWARD THE FAVOURITES, AND SHOW NO FAVOURITISM.

The proprietor of a ladies' school once received an invitation for one-half of her pupils to attend a flower show, but was a long time before she could decide how to pick out those who ought to be rewarded without hurting the feelings of those left behind. There were thirty pupils in the school, and fifteen were to be taken and the like number left at home. The following plan was the one hit upon:--The pupils were arranged in a row, four intended to go were placed first, five not intended next, and so on, as shown below, the letter A denoting those it was intended should partake of the offered pleasure, the letter B denoting those it was wished to leave out, and they were told when so arranged that the ninth girl, and each succeeding ninth, would be left at home.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
A A A A B B B B B A A B A A A

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
B A B B A A B B B A B B A A B

The counting commenced with No. 1, and went round and round consecutively, each ninth pupil being dropped out, as designated to stay at home. It will be seen that those to be left were dropped out in the following order:--9th, 18th, 27th, 6th, 16th, 26th, 7th, 19th, 30th, 12th, 24th, 8th, 22nd, 5th, 23rd, thus leaving fifteen only.

THE DISHONEST SERVANTS.

Three gentlemen, with their servants, had to cross over a river in a boat in which two passengers only could be transported at one time. The servants were known to have planned to murder and rob one or more of the masters if two servants were left with one master or three servants with two masters. The question to be decided was how these six persons were to cross so that the boat could be returned, and yet so that the servants on either side of the river should not outnumber the masters. The following is one of the several ways in which the difficulty might have been overcome:--Two servants go over first, one returns; two servants go over again, one again returning with the boat; two of the masters next go over, and a master and one of the previously taken servants returns; then two of the masters again go over, and the servant already crossed takes the boat back, leaving the three masters safely crossed; the servants are left to come over in any manner they choose.

LORD DUNDREARY'S FINGER PUZZLE TO COUNT ELEVEN FINGERS ON THE TWO HANDS.

Begin on one hand, and count the ten fingers throughout. Begin next time at the finger last counted in the first round, counting this time backwards--ten, nine, eight, seven, six--then holding up the other hand, say "And five are eleven."

UNIFORM RESULTS OF MULTIPLICATION.

The digits 15873 multiplied by 7 give .. .. 111111
" 31746 " 7 " .. .. 222222
" 47619 " 7 " .. .. 333333
" 63492 " 7 " .. .. 444444
" 79365 " 7 " .. .. 555555
" 95238 " 7 " .. .. 666666
" 126984 " 7 " .. .. 888888
" 142857 " 7 " .. .. 999999
Of course, it would need the digits 111111 to make .. 777777

TO ASCERTAIN A SQUARE NUMBER AT A GLANCE.

Every boy knows that a square number is a number produced by the multiplication of any number into itself; thus 7, multiplied by itself, gives 49 as a result, 49 consequently is a square number, 7 being termed the square root from which it springs. In high numbers the extraction of the square root is an affair of time and trouble, and after all the necessary calculations have been made it may perhaps be found that the number is not a square number. This unnecessary trouble may be saved if the following instructions are remembered:--Every square number ends with one of the figures 1, 4, 5, 6, or 9, or with two ciphers preceded by one or other of those figures. Again, every square number is either equally divisible by 4, or when divided by 4 will have a remainder of 1; thus, as shown above, the square of 7 is 49, which divided by 4 gives us a quotient 12 and 1 over; 64 again is a square number, and it is exactly divisible by 4.

TO DISTINGUISH COINS BY ARITHMETICAL CALCULATION.

Request some person to place in one of his hands a bronze coin and in the other a silver one, and to let no one know which hand contains either particular coin. This may be ascertained by the following calculation:--The calculator should assign an even number, say 4, to the bronze coin, and an odd number, say 7, to the silver coin. The person holding the coins should be requested to multiply the number assigned to the coin held in his right hand by an even number, and that assigned to the coin held in the left hand by an odd number. Instruct that the products of the two calculations be added together, and if the whole sum be even the silver coin will have been placed in the right hand, and the bronze coin in the left. If the result be an odd number, the reverse arrangement will of course have been made.

We will conclude this section by stating shortly some of the

PROPERTIES OF NUMBERS.

By a careful study of these properties many amusing arithmetical puzzles and numerical combinations may be arrived at:--

1. Every odd number multiplied by an odd number produces an odd
number.

2. Every odd number multiplied by an even number produces an even
number.

3. Every even number multiplied by an odd number produces an even
number.

4. An even number added to or subtracted from an even number, or an
odd number to or from an odd number, produces an even number.

5. An odd number added to or subtracted from an even number produces
an odd number.

6. The digits of the nine times multiplication table added together
make either 9 or 18 (twice 9), thus:--

9 × 1 = 9
9 × 2 = 18 or 8 plus 1 = 9
9 × 3 = 27 or 7 " 2 = 9
9 × 4 = 36 or 6 " 3 = 9
And so on to
9 × 11 = 99 or 9 plus 9 = 18

Then so on again up to 9 times 24, each table making 9, with the
exception of 9 times 22 =198=8+9+1=18. Indeed, the digits, added
together, of the product of any number multiplied by 9, will be found
to be 9 or a multiple thereof.

7. The digits 1 to 9 may be placed to form 362880 combinations; this
number divided by 9 gives 40320; these figures added together make 9.

8. If two numbers are divisible by any one number, their sum and
their difference will also be divisible by the same number.

9. If two numbers divisible by 9 be added together, the sum of the
figures will be either 9 or a multiple of 9.

CARD GAMES.

There is no knowing exactly when card-playing first made its appearance, or who introduced it. Long before Whist, Cribbage, or Piquet was heard of the natives of India and China amused themselves for many a long hour in card-playing. Though probably they did not restrict themselves to any particular rule or method, still, the enjoyment they derived from the game was, doubtless, quite equal to any that we have now. The old tale, that has so often been repeated, that Whist was invented purposely to entertain, during his moments of sanity, an English sovereign who had lost his reason, may or may not be true. All we really know is, that for more than two hundred years our grandmothers and grandfathers have spent many a happy hour at the card-table, sipping their toddy and playing their rubbers in really good earnest. As far as we are concerned, the toddy sipping may be with safety dispensed with, but not the earnestness; for with cards, almost more than any other amusement, it is utterly useless to play in a half-hearted sort of manner.

Everything, for the time, must be forgotten but the game, and into that the whole energy must be thrown. As all good players know, triflers are to be dreaded far more than inexperienced players. The latter, by practice, strict attention, the exercise of judgment, observation, and memory may soon become skilful players, while the former will never willingly be chosen as partners by good Whist players. It is said that good old Sir Roger de Coverley sent a messenger round every Christmas time with a pack of cards to all the cottagers on his estate, and if accompanied, as no doubt they were, with something useful and substantial, nothing could have been much more acceptable.

LONG WHIST.

Among all card games Whist is unequalled, and although no more than four players can join in one game, a whole roomful of people may easily play at the same time by simply dividing themselves into so many quartettes, a pack of cards being provided for each set of players.

For Long Whist four players are required, and a complete pack of fifty-two cards. The first step is for each player to draw a card from the pack, the two highest and the two lowest being partners, each player taking his seat opposite his partner. The cards are then shuffled by the "elder hand," who is the player to the left of the dealer, the post of dealer being allotted to the drawer of the lowest card; after which they are cut by the "younger hand," who is the player to the right of the dealer. Beginning with his left-hand neighbour, the whole pack is then dealt out to the players one by one, faces downward, until the last one is arrived at, which, though the property of the dealer, is turned up, displaying the trump suit. If dealt properly, every player will hold in his hand thirteen cards, which he is now at liberty to look at and arrange in order, the owner of each hand being in honour bound not to look at any cards but his own.

The object of the game is for each player to either make himself, or assist his partner in making, as many tricks as possible, so that they together may gain ten points, that number being game in Long Whist.

The player to the left of the dealer first leads a card which his left hand opponent follows with a card of the same suit; the next player does the same, until all four cards are upon the table, the trick belonging to the player of the highest card.

Should any one not be able to follow suit, he may either play a card from another suit, or give one of the trump suit, and may possibly, by adopting the latter method, secure the trick for himself and his partner from the hands of their adversaries.

The winner of the trick is entitled to the next lead, the others following him as they did the former leader, and thus the game goes on until the full thirteen tricks are made. The points gained by each side are then noted down, either on a cribbage board or entrusted to the memory of the players, after which another shuffling takes place, and the cards are again distributed, the game thus proceeding until one of the couples has obtained ten tricks, when the game is won.

Another way of scoring points, and one which greatly facilitates business, is that of counting the honours. The four court cards of the trump suit are called honours, and should any one be fortunate enough to have these four cards dealt to him in one hand, or if he and his partner have the cards between them, they can score four to their game. Three honours count for two; but should the honours be equally distributed--that is, should one set of partners have only two court cards between them--the other two cards of the same kind must necessarily be in the hands of their opponents, in which case the honours are said to be divided, and neither side reaps any advantage from them. Each set of partners must win six tricks, constituting "a book," before they may score any to the game.

It is possible, therefore, for a couple of players to gain ten or eleven points during one round, though such luck very rarely occurs. It is a much more common occurrence for five or six deals to be made before the winning of a game.

Although in playing Whist the beginner need know nothing more than the ordinary rules of the game to enable him to take a part, nothing but practice will make him a skilful player. It is only by experience he will learn how necessary it is for him to rigidly adhere to the rules of the game. Whist, like Chess, must be played properly, or not at all. It is, therefore, important that all who wish to be good Whist players should at once make themselves thoroughly acquainted with the rules of the game, and also learn what mistakes to avoid.

The following are technical terms used in Whist:--

_Ace._--Highest in play, lowest in cutting.

_Blue Peter._--A signal for trumps allowable in modern play. This
term is used when a high card is unnecessarily played in place of one
of lower denomination--as a ten for a seven, a five for a deuce, &c.

_Bumper._--Two games won in succession before adversaries have won
one; that is a rubber of full points. Five at Short Whist, ten at
Long.

_Cut._--Lifting the cards when the uppermost portion (not fewer than
three), is placed below the rest. The pack is then ready for the
dealer.

_Cutting in._--Deciding the deal by each player taking up not fewer
than three cards, and the two highest and two lowest become partners.
In case of ties, the cards must be cut again.

_Cutting out._--In case of other person or persons wishing to play,
the cut is adopted as before, when the highest (or lowest, as may be
agreed on), stands out of the game, and does not play.

_Call, The._--The privilege of the player at eight points asking his
partner if he holds an honour. "Have you one?" The partners having
eight points are said to _have the call_. When each side stands at
eight, the first player has the privilege. No player can call until
it is his turn to play.

_Deal._--The proper distribution of the cards from left to right,
face downwards.

_Deal, Fresh._--A fresh or new deal, rendered necessary by any
violation of the laws, or by any accident to the cards or players.

_Double._--Ten points scored at Long Whist before adversaries have
obtained five; or in Short Whist, five before three.

_Elder Hand._--The player to the left of the dealer.

_Faced Card._--A card improperly shown in process of dealing. It is
in the power of adversaries, in such cases, to demand a new deal.

_Finessing._--A term used when a player endeavours to conceal his
strength, as when having the best and third best (ace and queen) he
plays the latter, and risks his adversary holding the second best
(the king). If he succeed in winning with his queen, he gains a clear
trick, because if his adversary throws away on the queen, the ace
is certain of making a trick. The term finessing may be literally
explained by saying a player chances an inferior card to win a trick
with while he holds the king card in his hand.

_Forcing._--This term is employed when the player obliges his
adversary or partner to play his trump or pass the trick. As, for
instance, when the player holds the last two cards in a suit and
plays one of them.

_Hand._--The thirteen cards dealt to each player.

_Honours._--Ace, king, queen, and knave of trumps, reckoned in the
order here given.

_Jack._--The knave of any suit.

_King Card._--The highest unplayed card in any suit; the leading or
winning card.

_Lead, The._--The first player's card, or the card next played by the
winner of the last trick.

_Long Trumps._--The last trump card in hand, one or more, when
the rest are all played. It is important to retain a trump in an
otherwise weak hand.

_Loose Card._--A card of no value, which may be thrown away on any
trick won by your partner or adversary.

_Longs._--Long Whist, as opposed to Short.

_Lurch._--The players who make the double points are said to have
lurched their adversaries.

_Love._--No points to score. Nothing.

_Marking the game._--Marking the score apparent with coins, &c., or
with a whist-marker.

_Mis-deal._--A mis-deal is made by giving a card too many or too few
to any player, in which case the deal passes to the next hand.

_Nine Holes._--The side when the score, at a fresh deal, stands at 9,
must win, if at all, by points only; the honours do not count.

_No Game._--A game at which the players make no score.

_Opposition._--Side against side.

_Points._--The score obtained by tricks and honours. The wagering or
winning periods of the game.

_Quarte._--Four cards in sequence.

_Quarte Major._--A sequence of ace, king, queen, and knave.

_Quint._--Five successive cards in a suit; a sequence of five--as
king, queen, knave, ten, and nine.

_Rags._--Cards of no value, as the small numbers.

_Renounce._--Possessing no card of the suit led, and playing another
which is not a trump.

_Revoke._--Playing a card different from the suit led, though the
player can follow suit. The penalty for the error, whether made
purposely or by accident, is the forfeiture of three tricks. When a
Revoke is made the penalty should invariably be enforced.

_Rubber._--The best of three games, that is, two out of three.

_Ruffing._--Another term for trumping a suit other than trumps.

_Sequence._--Cards following in their natural order--as ace, king,
queen; two, three, four, &c. There may, therefore, be a sequence of
four, five, six, and so on.

_Single._--Scoring at Long Whist ten tricks before your adversaries
have scored five.

_See-Saw._--When each partner trumps a suit. For instance, A holds no
diamonds, and B no hearts. When A plays hearts, B trumps and returns
a diamond, which A trumps and returns a heart, and so on.

_Score._--The points gained in a game or rubber.

_Slam._--Winning every trick in a round.

_Shorts._--Short Whist as opposed to Long.

_Tenace._--Holding the best and third best of any suit led when last
player. Holding tenace; as king and ten of clubs. When your adversary
leads that suit, you win two tricks perforce. (_Tenace minor_ means
the second and fourth best of any suit).

_Treble._--Scoring five (at Short Whist) before your adversaries have
marked one.

_Tierce._--A sequence of three cards in any suit.

_Tierce Major._--Ace, king, and queen of any suit held in one hand.

_Trick._--The four cards played, including the lead.

_Trump._--The last card in the deal; the turn-up.

_Trumps._--Cards of the same suit as the turn-up.

_Ties._--Cards of like denomination--as two kings, queens, &c. Cards
of the same number of pips.

_Trumping Suit._--Playing a trump to any other suit led.

_Underplay._--Playing to mislead your adversaries; as by leading a
small card though you hold the king card of the suit.

_Younger Hand._--The player to the right of the dealer.

The following rules have frequently proved very valuable to beginners; we think, therefore, our own young readers who are at all ambitious to excel in Whist may as well have the benefit of them.

BOB SHORT'S RULES.

FOR FIRST HAND, OR LEAD.

1.--Lead from your strong suit, and be cautious how you change suits, and keep a commanding card to bring it in again.

2.--Lead through the strong suit and up to the weak, but not in trumps, unless very strong in them.

3.--Lead the highest of a sequence; but if you have a quart or quint to a king, lead the lowest.

4.--Lead through an honour, particularly if the game be much against you.

5.--Lead your best trump if the adversaries be eight, and you have no honour, but not if you have four trumps, unless you have a sequence.

6.--Lead a trump if you have four or five or a strong hand, but not if weak.

7.--Having ace, king, and two or three small cards, lead ace and king if weak in trumps, but a small one if strong in them.

8.--If you have the last trump, with some winning cards, and one losing card only, lead the losing card.

9.--Return your partner's lead, not the adversaries', and if you have only three originally, play the best; but you need not return it immediately when you win with the king, queen, or knave, and have only small ones, or when you hold a good sequence, have a strong suit, or have five trumps.

10.--Do not lead from ace queen or ace knave.

11.--Do not lead an ace unless you have a king.

12.--Do not lead a thirteenth card, unless trumps be out.

13.--Do not trump a thirteenth card, unless you be last player or want the lead.

14.--Keep a small card to return your partner's lead.

15.--Be cautious in trumping a card when strong in trumps, particularly if you have a strong suit.

16.--Having only a few small trumps, make them when you can.

17.--If your partner refuses to trump a suit of which he knows you have not the best, lead your best trump.

18.--When you hold all the remaining trumps, play one, and then try to put the lead in your partner's hand.

19.--Remember how many of each suit are out, and what is the best card left in each hand.

20.--Never force your partner if you are weak in trumps, unless you have a renounce or want the odd trick.

21.--When playing for the odd trick, be cautious of trumping out, especially if your partner be likely to trump a suit; make all the tricks you can early, and avoid finessing.

22.--If you take a trick and have a sequence, win with the lowest.

FOR SECOND HAND.

23.--With king, queen, and small cards, play a small one when not strong in trumps; but if weak, play the king. With ace, king, queen, or knave only, and a small card, play the small one.

FOR THIRD HAND.

24.--With ace and queen, play Her Majesty, and if she wins return the ace. In all other cases the third hand should play his best card when his partner has led a low one. It is a safe rule for third hand to play his highest.

FOR ALL THE PLAYERS.

25.--Fail not, when in your power, to make the odd trick.

26.--Attend to the game, and play accordingly.

27.--Hold the turn-up card as long as possible, and so keep your adversaries from a knowledge of your strength.

28.--Retain a high trump as long as you can.

29.--When in doubt, win the trick.

30.--Play the game fairly, keep your temper, and don't talk.

Supplied with the above directions, none of our young friends need hesitate to become one of four players at the whist-table, where, no doubt, they will soon distinguish themselves by their skill and dexterity.

This, however, will not be the case unless they resolve either to play well or not to play at all; and to do this, they must bear in mind that not only is it necessary to have a thorough knowledge of all the leading rules and principles of the game, but the little details, which are learnt only by degrees, must also receive due attention.

For instance, success greatly depends upon knowing when to return a partner's lead, how to secure the odd trick, and also how to finish the game.

A very common occurrence is for a well-played game to be spoilt by the last two or three tricks being played badly; and the ending of the game is almost more important than the beginning.

An inexperienced player, elated, perhaps, by a little seeming success, which, no doubt, has really been attributable to the good playing of his partner, has often been known to spoil the end of a game by his bad playing.

Very slow calculating players are by no means regarded in the light of acquisitions at a card-table; still, as compared with rash, thoughtless players, they are very much the safer partners.

Most of the long established laws of Whist, which must be thoroughly mastered and committed to memory by all learners, in order that they may be carried into practice continually, are as follows:--

LAWS OF LONG WHIST.

THE RUBBER.

1.--The rubber is the best of three games. If the first two games are won by the same players the third game is not played.

2.--A game consists of ten points (five in Short Whist). Each trick above six counts one point.

3.--Honours, _i.e._, ace, king, queen, and knave of trumps, are thus reckoned:--

If a player and his partner, either separately or conjointly, hold--
1st. The four honours, they score four points.
2nd. Three of the honours, they score two points.
3rd. Two honours only, they do not score. (In Short Whist honours
do not count.)

4.--Those players who at the commencement of a deal are at the score of nine cannot score honours.

5.--The penalty for a revoke takes precedence of all other scores; tricks score next; honours last.

6.--Honours, unless claimed before the trump card of the following deal is turned up, cannot be scored.

7.--To score honours is not sufficient: they must be called at the end of the hand; if so called, they may be scored at any time during the game.

8.--If an erroneous score be proved, such mistake can be corrected prior to the conclusion of the game in which it occurred, and such game is not concluded until the trump card of the following deal has been turned up.

9.--If an erroneous score, affecting the amount of the rubber, be proved, such mistake can be rectified at any time during the rubber.

10.--In cutting, the ace is the lowest card.

11.--In all cases every one must cut from the same pack.

12.--Should a player expose more than one card, he must cut again.

13.--In cutting for partners, two players cutting cards of equal value, unless such cards are the two highest, cut again; should they be the two lowest, a fresh cut is necessary to decide who shall deal.

14.--Three players cutting cards of equal value cut again.

SHUFFLING.

1.--The pack must be shuffled above the table, but not so that the cards can be seen.

2.--The pack must not be shuffled during the play of the hand.

3.--The dealer's partner must collect the cards for the ensuing deal, and has the first right to shuffle that pack.

4.--Each player, after shuffling, must place the cards, properly collected and face downwards, to the left of the player about to deal.

5.--The dealer has always the right to shuffle last; but should a card or cards be seen during his shuffling or any other time, he must re-shuffle.

6.--Each player deals in his turn; the right of dealing goes to the left.

7.--The player on the dealer's right cuts the pack, and in dividing it must not leave fewer than four cards in either packet; if, in cutting, a single card be exposed, or if there be any confusion of the cards, there must be a fresh cut.

8.--When a player whose duty it is to cut has once separated the pack, he must neither re-shuffle nor re-cut the cards.

9.--After the pack is cut, should the dealer shuffle the cards he loses his deal.

10.--If any card, except the last, be faced in the pack, or if the pack prove to be imperfect, there must be a new deal.

11.--A misdeal loses the deal.

12.--The trump card must be left on the table until the first trick has been won.

13:--A revoker must give three tricks to his opponent.

14.--When a revoke has been made the opponents may search all the tricks.

15.--A revoke cannot be claimed after the cards have been cut for the next deal.

16.--Bystanders should be silent.

The following general principles will be found to be of very great value:--

FIRST HAND.

1.--Lead from your strongest suit.

2.--Lead the highest of a head sequence.

3.--Lead the highest of a numerically weak suit.

4.--Try to avoid changing suits.

5.--In the second round of a suit return the lowest of a four suit, the highest of a three suit.

SECOND HAND.

6.--The second hand player in the first round of a suit should generally play the lowest card, and also win with the lowest of a sequence.

7.--If you do not head a trick you should throw away with your lowest card.

8.--Young players often make the mistake of imagining that it does not signify which card they play when they hold only small cards or cards in sequence.

9.--They have still to learn that a reason ought to exist for the playing of every card on the table, and that the winning of a single trick is not all that ought to be taken into consideration; the information afforded to one's partner must also be thought of.

THIRD HAND.

10.--Play your highest card third hand. Presuming that your partner, who may lead a small card, plays from his strong suit, meaning to get the winning cards of it out of his way, you therefore play your highest, remembering that you play the lowest of a sequence.

11.--When your partner leads a high card, however, the case is different. You must not put ace on your partner's king, thus parting with ace and king in one trick.

12.--If you think that your partner has led from a weak suit, you may then finesse king, knave, &c., or pass his card altogether, so as not to give up the entire command of the suit; but if you are not sure whether his card is intended to signify strength or weakness, do not finesse.

FOURTH HAND.

13.--Less skill is required by the fourth player than any of the others; all he has to do is to try to beat the three cards on the table before him, and thus win the trick, unless, of course, it has already been taken by his partner, who has either played the highest card or trumped. In that case the player should play a low one of the same suit, or if he cannot do that he should discard.

When not able to follow suit, you should discard from your weakest suit; indeed, the fact of your discarding originally from any suit is an intimation to your partner that you are weak in that particular suit. Natural discards may be distinguished from such as are forced by taking into consideration the aspect of the game at the time of the discard.

If the person discarding has been playing a strong game, or leading trumps, you may be sure that the discard was from a weak suit; while, on the other hand, any one discarding who has not shown strength most likely does it to conceal weakness. The best use that can be made of trumps is a matter that is by no means learnt all at once. The advantage generally acknowledged to be the greatest in the possession of a hand strong in trumps is to draw the adversaries' trumps for the bringing in of your own or your partner's long suit. At the same time, should you be weak in every suit but trumps, you have no alternative but either always leading trumps or leading from a weak suit. As a general rule, it is only right to lead trumps when strong in them, therefore your partner's lead of trumps should be returned immediately. Still, a player, however strong in trumps, should not use them recklessly, but remembering that they are meant to disarm the opponents, should employ them as much as possible for that purpose. Such advice, we ought to remark, is only serviceable among sound players; should you have an inexperienced partner, the best thing to be done is to make as many tricks as you can, and not attempt to play scientifically.