Conundrums, Riddles and Puzzles / Containing one thousand of the latest and best conundrums, gathered from every conceivable source, and comprising many that are entirely new and original

by Dean Rivers

Take any number, divide it by 9, and name the remainder. Multiply the number by some number which I name, and divide the product by 9, and I will name the remainder.

Method.—To tell the remainder, I multiply the first remainder by the number by which I told them to multiply the given number, and divide this product by 9. The remainder is the second number obtained.

Think of a number greater than 3, multiply it by 3; if even, divide it by 2; if odd, add 1, and then divide by 2. Multiply the quotient by 3; if even, divide by 2; if odd, add 1, and then divide by 2. Now divide by 9 and tell the quotient without the remainder, and I will tell you the number thought of.

Method.—If even both times, multiply the quotient by 4; if even 2d and odd 1st, multiply by 4 and add 1; if even 1st and odd 2d, multiply by 4 and add 2; if odd both times, multiply by 4 and add 3.

Suppose it were possible for a man in Cincinnati to start on Sunday noon, when the sun is in the meridian, and travel westward with the sun so that it might be in his meridian all the time. Now it was Sunday noon when he started, it has been noon with him all the way round, and is Monday noon when he returns. The question is, at what point did it change from Sunday noon to Monday noon?

Take any number, subtract the sum of the digits, strike out any digit from the remainder, tell me the sum of the remaining digits, and I will tell you the digit struck out.

Method.—Subtract the “sum of the remaining digits” from the smallest multiple of nine greater than “the sum.” The remainder will be the digit struck out.

In the bottom of a well, 45 feet deep, there was a frog which commenced traveling toward the top. In his journey he ascended 3 feet every day, but fell back 2 feet every night. In how many days did he get out?

Method.—He gains 1 foot a day, and in 42 days he is 3 feet from the top; and on the 43d day he reaches the top.

Think of any three numbers less than 10. Multiply the first by 2 and add 5 to the product. Multiply this sum by 5 and add the second number to the product. Multiply the last result by 10 and add the third number to the product; then subtract 250. Name the remainder and I will name the numbers thought of and in the order in which they were thought of.