The (almost really) Complete Works of Lewis Carroll

Questions for Solution: 12650

Source: The Educational Times, February 1895

Solutions by D. Biddle, Professor Radhakishuan, and others were published in Mathematical Questions and Solutions, from the “Educational Times”, LXIII, 1895, from where the question is taken here, too. But they all miss the much simpler approach (which Carroll probably had in mind) of writing the number as 9n+r with 0≤r<9. Then r can be easily calculated from the two digits tacked on and the two remainders, while the third figure of the last number is just n.

Other version: Number-guessing

12650. (C. L. Dodgson, M.A.)—To discover the rule by which the following puzzle is worked. It is best exhibited as a dialogue.

A. Think of a number less than 90.—B. I have done so.

A. Tack on to it any digit you like, from 0 to 9. Which shall it be?—B. I have tacked on a 7.

A. Now divide by 3. What is the remainder?—B. It is 2.

A. Tack on to the quotient any digit you like.—B. I have tacked on 4.

A. Divide by 3. What is the remainder?—B. It is 1.

A. And what is the third figure from the end?—B. It is 8.

A. (Instantly rejoins) Then the number you thought of was 76.