A Rapid Sum - Futility Closet

A Rapid Sum

From Lewis Carroll’s diary, Feb. 5, 1856:

Varied the lesson at the school with a story, introducing a number of sums to be worked out. I also worked for them the puzzle of writing the answer to an addition sum, when only one of the five rows have been written: this … astonished them not a little.

He had started by writing an arbitrary number:

21879

Then he asked the students to call out a second five-digit number. Carroll added a third, the students shouted a fourth, and Carroll added a fifth and immediately wrote the sum:

How did he do this?

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In writing the third and fifth numbers, he just wrote the complement of 9 for each digit in the number immediately above. When this is done, the sum can be found immediately by taking the first number, subtracting 2 from its last digit, and inserting a 2 at the front of the number.

May 21, 2019May 20, 2019 | Science & Math