Part 15 (1/2)

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Here is a neat little trick with three dice I ask you to throw the dice withoutthem Then I tell you to multiply the points of the first die by 2 and add 5; then multiply the result by 5 and add the points of the second die; then multiply the result by 10 and add the points of the third die You then give me the total, and I can at once tell you the points throith the three dice How do I do it? As an example, if you threw 1, 3, and 6, as in the illustration, the result you would give me would be 386, from which I could at once say what you had thrown

387--THE VILLAGE CRICKET MATCH

In a cricket leton, the latter had the first innings Mr Dumkins and Mr Podder were at the wickets, when the wary Dumkins made a splendid late cut, and Mr Podder called on hiilant u six short runs in all What nuley Dell took their turn at the wickets their chales The latter ue to ”co,” with the result that the observant spectators applauded them for as supposed to have been three sharp runs But the umpires declared that there had been two short runs at each end--four in all To what extent, if any, did this les's total?

388--SLOW CRICKET

In the recent county match between Wessex and Nincomshi+re the for put out a fewstumps The play was so slow thatawakened by one of the officials clearing the ground, we learnt that two -before-wicket for a coht for a co; and the others were all bowled for 3 runs each There were no extras We were not told which of the men was the captain, but he e of his team What was the captain's score?

389--THE FOOTBALL PLAYERS

”It is a glorious game!” an enthusiast was heard to exclaim ”At the close of last season, of the footballers of my acquaintance four had broken their left arht arm sound, and three had sound left arms” Can you discover from that statement what is the smallest number of players that the speaker could be acquainted with?

It does not at all follow that there were as many as fourteen men, because, for exaht also be the tho had sound right arms

390--THE HORSE-RACE PUZZLE

There are nothe old puzzle of the captain who, having to throw half his crew overboard in a stored to draw lots, but so placed the men that only the Turks were sacrificed, and all the Christians left on board, we do not stop to discuss the questionablewith a rims are to make an equitable division of a barrel of beer, we do not object that, as total abstainers, it is against our conscience to have anything to do with intoxicating liquor Therefore Ia puzzle that deals with betting

Three horses--Acorn, Bluebottle, and Capsule--start in a race The odds are 4 to 1, Acorn; 3 to 1, Bluebottle; 2 to 1, Capsule No much must I invest on each horse in order to win 13, no , as an example, that I betted 5 on each horse Then, if Acorn won, I should receive 20 (four times 5), and have to pay 5 each for the other two horses; thereby winning 10 But it will be found that if Bluebottle was first I should only win 5, and if Capsule won I should gain nothing and lose nothing This will make the question perfectly clear to the novice, who, likeof the fraternity who profess to be engaged in the noble task of ”i the breed of horses”

391--THE MOTOR-CAR RACE

Sometimes a quite simple statement of fact, if worded in an unfamiliar manner, will cause considerable perplexity Here is an example, and it will doubtless puzzle some of my more youthful readers just a little I happened to be at a motor-car race at Brooklands, when one spectator said to another, while a nu round and round the circular track:-- ”There's Gogglesmith--that man in the white car!”

”Yes, I see,” was the reply; ”but howin this race?”

Then came this curious rejoinder:-- ”One-third of the cars in front of Gogglesive you the answer”

Now, can you tell howin the race?

PUZZLE GAMES

”He that is beaten may be said To lie in honour's truckle bed” HUDIBRAS

It ame is a contest of skill for two or more persons, into which we enter either for a to be done or solved by the individual For example, if it were possible for us so to a with the first or second , then it would cease to be a ga and uninfor play is not understood, a puzzle ame Thus there is no doubt children will continue to play ”Noughts and Crosses,” though I have shown (No 109, ”_Canterbury Puzzles_”) that between two players who both thoroughly understand the play, every game should be drawn Neither player could ever win except through the blundering of his opponent But I as

The exaames, but, since I show in every case how one player may win if he only play correctly, they are in reality puzzles Their interest, therefore, lies in atte method of play

392--THE PEBBLE GAME

Here is an interesting little puzzle game that I used to play with an acquaintance on the beach at Slocomb-on-Sea Two players place an odd number of pebbles, ill say fifteen, between them Then each takes in turn one, two, or three pebbles (as he chooses), and the winner is the one who gets the odd nuht, you win If you get six and he gets nine, he wins Ought the first or second player to win, and how? When you have settled the question with fifteen pebbles try again with, say, thirteen

393--THE TWO ROOKS

This is a puzzle gale rook The first player places his rook on any square of the board that he may choose to select, and then the second player does the sa to capture the opponent's rook But in this ga captured That is to say, if in the diagram it is Black's turn to play, he cannot 's rook's square, because he would enter the ”line of fire” when passing his king's bishop's square For the sahth squares Now, the game can never end in a draw Sooner or later one of the rooks must fall, unless, of course, both players co is ridiculously simple when you know it Can you solve the puzzle?

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394--PUSS IN THE CORNER

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This variation of the last puzzle is also played by two persons One puts a counter on No 6, and the other puts one on No 55, and they play alternately by re the counter to any other number in a line If your opponent moves at any time on to one of the lines you occupy, or even crosses one of your lines, you immediately capture hiame

A moves frooes to 15; A retreats to 26; B retreats to 13; A advances to 21; B retreats to 2; A advances to 7; B goes to 3; A o to 4; A establishes himself at 11, and B must be captured next move because he is compelled to cross a line on which A stands Play this over and you will understand the gaame is this: Which player should win, and how many moves are necessary?

395--A WAR PUZZLE GAME

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Here is another puzzle gaeneral, places a counter at B, and the other player, representing the enemy, places his counter at E The Britisherone of the roads to the next town, then the enemy moves to one of his nearest towns, and so on in turns, until the British general gets into the sah eacha road to the next town only, and the second player eneral (as we should suppose, froy of real life) must infallibly win But how? That is the question

396--A MATCH MYSTERY

Here is a little game that is childishly siation

Mr Stubbs pulled a small table between himself and his friend, Mr Wilson, and took a box of matches, from which he counted out thirty

”Here are thirty matches,” he said ”I divide them into three unequal heaps Let me see We have 14, 11, and 5, as it happens Now, the two players draw alternately any number froame That's all! I will play with you, Wilson I have formed the heaps, so you have the first draw”

”As I can draw any number,” Mr Wilson said, ”suppose I exhibit my usual moderation and take all the 14 heap”

”That is the worst you could do, for it loses right away I take 6 fro two equal heaps of 5, and to leave two equal heaps is a certain ith the single exception of 1, 1), because whatever you do in one heap I can repeat in the other If you leave 4 in one heap, I leave 4 in the other If you then leave 2 in one heap, I leave 2 in the other If you leave only 1 in one heap, then I take all the other heap If you take all one heap, I take all but one in the other No, you must never leave two heaps, unless they are equal heaps and ain”

”Very well, then,” said Mr Wilson ”I will take 6 from the 14, and leave you 8, 11, 5”

Mr Stubbs then left 8, 11, 3; Mr Wilson, 8, 5, 3; Mr Stubbs, 6, 5, 3; Mr Wilson,4, 5, 3; Mr Stubbs, 4, 5, 1; Mr Wilson, 4, 3, 1; Mr Stubbs, 2, 3, 1; Mr Wilson, 2, 1, 1; which Mr Stubbs reduced to 1, 1, 1

”It is now quite clear that I must win,” said Mr Stubbs, because youyou the last match You never had a chance There are just thirteen different ways in which the rouped at the start for a certain win In fact, the groups selected, 14, 11, 5, are a certain win, because for whatever your opponent roup you can secure, and so on and on down to the last match”

397--THE MONTENEGRIN DICE GAME

It is said that the inhabitants of Montenegro have a little dice gaation The two players first select two different pairs of odd nuher than 3) and then alternately toss three dice Whichever first throws the dice so that they add up to one of his selected numbers wins If they are both successful in two successive throws it is a draw and they try again For example, one player may select 7 and 15 and the other 5 and 13 Then if the first player throws so that the three dice add up 7 or 15 he wins, unless the second ets either 5 or 13 on his throw

The puzzle is to discover which two pairs of nuive both players an exactly even chance

398--THE CIGAR PUZZLE

I once propounded the following puzzle in a London club, and for a considerable period it absorbed the attention of theof it, and considered it quite impossible of solution And yet, as I shall show, the answer is remarkably simple