Can you find one five figure number, with distinct digits between 1 and 9, which satisfies all four of the following equations?

SNAKE * 2 = MERES
COYPU * 8 = POODLE
TIGER * 13 = BEWAIL
OKAPI * 14 = HIJACK

Repeated letters within an equation refer to the same digit. The same letter appearing in different equations does not necessarily refer to the same digit.

The puzzle can be solved from just two equations. The other two are for fun/reference.

This is similar to Can't see the wood for the trees

The five figure number is 48537.
(Not all products are composed of the digits 1 to 9, as the R in MERES and the W in BEWAIL use the digit 0, but this limitation seems to have been limited to the factors).

SNAKE *  2 =  MERES
48537 *  2 =  97074

COYPU *  8 = POODLE
48537 *  8 = 388296

TIGER * 13 = BEWAIL
48537 * 13 = 630981

OKAPI * 14 = HIJACK
48537 * 14 = 679518


As I had done with "Can't see the wood for the trees", I submit a few more "animal magic" equations:

TARIN *  3 = STRESS
48537 *  3 = 145611
(tarin - a small yellow singing bird with an ash colored head)

TENCH *  4 = ASTATE
48537 *  4 = 194148
(tench - a freshwater dace-like game fish)

BISON *  5 = ABACUS
48537 *  5 = 242695
(bison - a humpbacked shaggy-haired wild ox)

CONEY * 11 = NEEDLY
48537 * 11 = 533907
(coney - a rabbit; also, a black-spotted fish with reddish fins) 

48537 is a composite of the factors 3² and 5393, so we can also venture into the product of fractions:

MOUSE * 1/3 = PIPER
48537 * 1/3 = 16179

ANGUS * 1/9 = GURU
48537 * 1/9 = 5393

Edited on March 22, 2008, 6:47 am

Posted by Dej Mar on 2008-03-22 01:33:31