d_n denotes the incidence of a single digit d precisely n times. For example, 4₆7₃8₅ would denote 44444477788888.

Find the value of each of A, B, C, D, E and F satisfying this equation:

2_A3_B5_C + 3_D5_E2_F = 5₃7₂8₃5₁7₃

With two numbers sum to a third this is pretty easy.
I solved it by writing out 5₃7₂8₃5₁7₃
and then figuring out where the other digits had to fall.
A=5 B=4 C=3 D=3 E=5 F=4 quickly becomes obvious and disappointingly easy.

A problem with the sum of 3 numbers might be more interesting especially if there is more than one way to sum to a digit and if potential carries muddles things up.

Posted by Jer on 2013-09-16 13:59:00