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By Frederick Milnes Edge

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Extra resources for The exploits and triumphs in Europe of Paul Morphy, the chess champion

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Yesterday you dived and found only 6 pearls, which you put on a string, knowing that with just two cuts (as shown below) your partner, who makes up the pearl necklaces, could obtain any number of pearls up to all 6: 1 by itself 2 as a pair 3 as a trio 4 as 3 + 1 5 as 3 + 2 6 as 3 + 2 + 1 Today you have found 23. Where, m the string of 23, should you make four ruts in order to be able to obtain any number between 1 and 23? 34 4> & FACTORIAL FORTY There are foui numbers between 1 and 40 (inclusive) that singly or in different combinations, with a plus or minus sign placed between them can total every number between 1 and 40.

The initial 1, which must be ignored) is 6. This shows that there are 6 possible combinations of any two of four. li there is a chance element, the way to find out the chances of a specific two turning up from a total of four is to look at row 4 and compare the second along (6 again) with the total of all the numbers in the row . 8. I have filled in the iirst few TOWS oi the Pascal's Triangle for you Can you complete the other rows as tar as shown on this page? >ASCAIS TRIANGLE Blaise Pascal was a French mathematician and philosopher; he was born in 1623 One ot hi; many great contributions to math was his part m laying the foundations of probability theory, and it was during his research in 44 this field that he made use of a special ti langular pattern of numbers The pattern can be tiaced back to the ancient Chinese - but is now generally called Pascal's Triangle because oi the ingenious applications he found for it.

With B and C, value 2 of C appears 24 times, allowing B to win. With C and D the answer is also 24 The fact thai C beats D is shown in dij'gramatic form in the table below A similar table can b e completed to show that D beats A 24 out of 36 times too Key Dice C Loses • Dice C Wins 63 INDEX Calculating the odds, 44 5, 61 Coin Solitaire, 22-3, 55 Combi-cards, 20-1, 54 Combination lock, 11, 50 Continuous paths, 12-13, 51 Crossroads, 33, 58 Cutting the necklace, 34, 58 Dicey problems, 45, 61 Eight-point star, 17, 53 Eighteen-point problem, 24-5, 55 Eleven-point problem, 24, 56 Emperor of Rome, 28, 57 Factorial forty, 35, 58 Finding the key, 10-11, 50 From pillar to post, 30-1, 57 Gaussian curve, 45 Gridlock, 32, 58 Husbands and wives, 40-1, 60 Interplanetary courier, 38-9, 59 Jumping coins, 26—7, 56 Jumping coins formula, 57 Key to the keys, 10, 50 Life or death, 28-9, 57 Lion's lunch, 29, 55 Lucky dice, 49, 63 Lucky spinner, 48-9, 63 Magic cross, 16, 53 Magic hexagon, 17, 53 Magic numbers, 16-17, 53 Magic numbers 2, 18-19, 54 Magic squares, 18-19, 5 3 - 4 Magic wheel, 16-17, 53 Match blocks, 8 - 9 , 50 Missing links, 35, 58 Money problems, 22-3, 55 Octopus handshake, 42-3, 61 Pascal's triangle.

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