Solution to Enigma No. 1530

28 January 2009

Answer: The 5-digit number represented by DALEY is 10348.

The winner is John Laurenson of Wellington, New Zealand. There were 358 entries.

Worked answer

M cannot be 0 or 5 because then M = Y.

Since D must be 1, M cannot be 1 or 7, as if M = 7, Y = 1.

A must be 2 or 0. If A = 2, TOM must be greater than 923, and since 0 cannot be 2 it must be greater than 933.

Since, therefore, L cannot be 0, DALEY must be greater than 12344 and TOM must be greater than 952.

M cannot be 2 or 9 or 4 (if M = 4, Y = 2) or 3 (if M = 3, Y = 9) and can only be 8 or 6.

TOM = 986, 978, 976, 968, 958, 956

DALEY = 12818, 12714, 12688, 12584, 12454, 12428

If A = 0 and T = 8, TOM must lie between 843 and 823; M cannot be 8 or 6 (if M = 6, Y = 8) and can only be 9, 4, 3 or 2.

TOM = 843, 842, 839, 834, 832, 829, 824, 823

DALEY = 10959, 10946, 10907, 10842, 10816, 10777, 10712, 10699

If A = 0 and T = 7, TOM must be greater than 786 and M cannot be 9 (if M = 9, Y = 7).

Therefore TOM = 798, 796, 794, 793, 792, and

DALEY = 10374, 10348, 10322, 10309, 10296

So only with TOM = 796 and DALEY = 10348 are all the eight digits different as required.

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