Sunday Times Teaser 2539 – Doubling Up
by DJT Hogg
Published: 22 May 2011 (link)
One day at school I found myself in charge of two classes. Faced with 64 pupils and only 32 desks, I gave each child a different whole number and told them the highest number must share with the lowest, the second highest with the second lowest, etc. When they had sorted themselves into pairs, I got each child to multiply their own number by that of their desk-mate. They discovered all the products were the same. In fact I chose the original numbers so that this common product would be as low as possible.
What was the common product?