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

BRIAN x 2 = CONGA
LINDA x 3 = NAILER
LEVIK x 4 = VARIED
CORAL x 6 = NESTED

Repeated letters within an equation indicate the replication of digits. However, the same letter in different equations does not necessarily refer to the same digit.

Describing the number as "abcde" the following can be found:

abcde <= 49999 (1st equation)

abcde >= 33334 (2nd equation)

therefore a = 3 or 4.

The maximum abcde x 3 = 149997

therefore from the 2nd equation N=1 and the middle term c=1. Answer: ab1de

From this, when used in the second equation we find the N will not carry any value to the next column when multiplied by 3 - so LI x 3 = NAI.  This will work only if I=5. So b=5. Answer: a51de

Continuing with 2nd equation L5 x 3 = 1A5 with L = 3 or 4. If L=3 then A=0 which it cannot due to A's appearance in the word LINDA and 0 not being an available value.  Thus L=4 and A=3, (a=4, e=3). Answer:451d3.

The first equation forces d=6.

Final answer using only first two equations: 45163

Edited on December 8, 2006, 10:11 am

Posted by Leming on 2006-12-08 10:08:45