Mathematical Mystery Unraveled

Integer Repetition Table

When I first came across this table I was hoping that it had some kind of mystical purpose that would allow you to decode some fancy numbers, like trigonometric functions or logarithms or square roots or something. I mean those Finns are inscrutable, who knows what's running through their heads. Alas, that is not the case. It is simply a way for teachers to assign a whole batch of simple arithmetic exercises to their students.

The answer comes to us from jpgordon on the Wikipedia Reference Desk:

"Mr. Reinhard now tells us a very simple procedure to demonstrate as many and different exercises in arithmetic with pure numbers to all the students through all basic operations up to the unlimited number range. His method is based on a scheme consisting of 81 squares, in which the basic numbers 1 to 9 are set in nine vertical and just as many horizontal rows so that the first two are never repeated in two successive numbers. Various combinations and result in many thousands of exercise examples..."