by Bill Graham

Hardly anybody thinks of mathematicians as interesting characters. Nonetheless, there are many anecdotes about mathematicians that are fascinating.

Johann Carl Friedrich Gauss lived about 200 years ago. As a little boy, he attended school in a one-room schoolhouse in Germany. One day, as the students were restless, the headmaster was losing his patience. He got angry at the class, and needing a respite, told the students to take out their slates and add all the numbers from one to 100.

After a minute or so of peace and quiet, he noticed young Gauss no longer working on his sum. Angrily, he told him to follow directions and complete the addition. Young Gauss said he was finished. The headmaster, about to make an example of the little upstart, told him to bring his slate up to the front of the room.

He was astonished to find the correct answer of 5,050. Gauss, with his brilliant and analytical mind, had noticed that the two end numbers, one and 100, had a sum of 101. After that, the next two end numbers, two and 99, had a sum of 101. There were 50 pairs of numbers with a sum of 101, so Gauss multiplied 101 times 50 and arrived at the answer of 5,050. That’s pretty amazing thinking for a little kid.

As an adult, Gauss made the first new discovery in Euclidian geometry in 2,000 years; that is, that a circle can be divided into 17 equal arcs. (Not much use around the house, but mathematicians loved it.) He applied his brilliance to astronomy and calculated the orbit of the newly discovered asteroid, Ceres. History has awarded him the distinction of being considered one of the greatest mathematicians of all time, along with Archimedes and Newton. Maybe all this has something to do with the following puzzle.

Never do this to a book!

I noticed an unusual thing about a book. (This book had no redeeming features except to provide this puzzle.) I tore out one page and noticed that the sum of the remaining page numbers was exactly 10,000. How many pages did the book have originally, and what page did I tear out?