# New Scientist Enigma 999 – Combined Celebrations

*by Susan Denham*

#### From Issue #2154, 3rd October 1998

To celebrate next week’s 1000th edition of Enigma, we each made up an Enigma. Each one consisted of four clues leading to its own unique positive whole number answer. In each case none of the four clues was redundant. To avoid duplication, Keith made up his Enigma first and showed it to Susan before she made up hers.

The two Enigmas were meant to be printed side-by-side but the publishers have made a (rare) error and printed the clues in a string:

(A) It is a three-figure number;

(B) It is less than a thousand;

(C) It is a perfect square;

(D) It is a perfect cube;

(E) It has no repeated digits;

(F) The sum of its digits is a perfect square;

(G) The sum of its digits is a perfect cube;

(H) The sum of all the digits which are odd in Keith’s

answer is the same as the sum of all the digits

which are odd in Susan’s.

Which four clues should have formed Keith’s Enigma, and what was the answer to Susan’s?