The next calculation, 4 and 10, gives us a total 14. The ten is, in this case, cancelled, and the fourteen regarded as four, which will be found to be the correct indicator for the next shifting.
It looks more mystifying if the performer be blindfolded, for he can tell the position of the cards with his fingers. Keeping his hand on the card, he asks, “Will you please tell me how many cards were shifted?” As soon as the answer is given, he exhibits the card, and can continue the trick as long as he pleases.
[5.] Find 16 numbers in arithmetical progression (common difference 2) whose sum shall be equal to 7552, and arrange them in 4 columns, 4 numbers in each column—or, in other words, arrange in a square of 16 numbers that when added vertically, horizontally, or diagonally, the sum of each 4 numbers will amount to 1888.
SOME CURIOUS NUMBERS.
If the number 37 be multiplied by 3, or any multiple of 3 up to 27, the product is expressed by three similar digits. Thus—
- 37 × 3 = 111
- 37 × 6 = 222
- 37 × 9 = 333
The products succeed each other in the order of the digits read downwards, 1, 2, 3, etc., these being multiplied by 3 (their number of places) reproduce the multiplicand of 37.
- 1 × 3 = 3
- 2 × 3 = 6
- 3 × 3 = 9