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 If it be multiplied by multiples of 3, beyond 27, this peculiarity is continued, except that the extreme figures taken together represent the multiple of 3 that is used as a multiplier. Thus-- 37 × 30 = 1110, extreme figures, 10 37 × 33 = 1221 " " 11 37 × 36 = 1332 " " 12 The number 73 (which is 37 inverted) multiplied by each of the numbers of arithmetical progression 3, 6, 9, 12, 15, etc., produces products terminating (unit’s place) by one of the ten different figures, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. These figures will be found in the reverse order to that of the progression, 73 × 3 produces 9, by 6 produces 8, and 9 produces 7, and so on. Another number which falls under some mysterious law of series is 142,857, which, multiplied by 1, 2, 3, 4, 5, or 6 gives the same figures in the same order, beginning differently; but if multiplied by 7, gives all 9’s. 142,857 multiplied by 1 = 142,857 " " 2 = 285,714 " " 3 = 428,571 " " 4 = 571,428 " " 5 = 714,285 " " 6 = 857,142 " " 7 = 999,999 Multiplied by 8, it gives 1,142,856, the first figure added to the last makes the original number--142,857. The vulgar fraction 1/7 = ·142,857. The following number, 526315789473684210, if multiplied as above, will, in the product, present the same peculiarities, as also will the number 3448275862068965517241379310.