Hi-Lo Cryptogram
In the cryptogram above, the L position indicates a digit from the set and the positions indicate a digit from the set . All digits in the H positions are unique.
While there is not a unique way to fill in the cryptogram, the H in the sum's result can only be one particular value. What is it?
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1 solution
The only way for two unique numbers from the set { 5 , 6 , 7 , 8 , 9 } to be added together and get a ones digit of 1 is with 5 and 6; 5 + 6 = 1 1 . Therefore the ones digits must be 5 and 6 in some order, and there is a carry digit of 1 into the tens column.
The smallest possible sum for the tens column is if the H digit is 7 (5 and 6 were already used) and if the L digit is 1. Including the carry digit, that results in a sum of 1 + 7 + 1 = 9 . If either the H or L digit is any larger it will result in a carry into the hundreds column, which is not part of the sum. Therefore the tens column must sum to 9.