The only base-10 integers OPEN and ERROR such that each letter represents one distinct decimal digit are OPEN = 8276 and ERROR = 74484. 74484 is 9 times 8276, thus A=9 or T=9.
Given the partial product REAPS as a multiple of OPEN with each letter representing one distinct digit REAPS would need be 41380 or 57932, yet with OPEN=8276 and ERROR = 74484,
REAPS would need be of the form 47A2S. Neither 41380 nor 57932 is of the form 47A2S, thus there is no solution with the givens.
Posted by Dej Mar
on 2011-10-08 03:00:53