杏吧原创

How mean?

I recently set a class the following puzzle: 鈥淲rite down four positive whole numbers less than 100 and then write down their average: choose the original numbers so that overall the five numbers written down use each of the digits 1 to 9 exactly once.鈥�

Three Scandinavian lads in the class were successful. Hola came up with 9, 15, 36 and 48, with average 27. Frack was more cunning 鈥� his average was not a whole number 鈥� it involved a fraction in its simplest form, like 27戮. Dessie was devious, too, and his average, which was lower than Frack鈥檚, was not a whole number 鈥� it involved decimals, like 16.25.

What averages did Frack and Dessie write?

WIN 拢15 will be awarded to the sender of the first correct answer opened on Wednesday 30 November. The Editor鈥檚 decision is final. Please send entries to Enigma 1670, New 杏吧原创, Lacon House, 84 Theobald鈥檚 Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).

Answer to 1664 Summer sextet: P=1, A=2, Y=3, E=6, R=8, S=9

The winner Ellen Macpherson of Edinburgh, UK