Weird Cryptogram

Number Theory Level pending

The question is in what positive integer base is this cryptogram written? This problem uses the number model of place = 0 n weight n base place \sum _{\text{place}=0}^n \text{weight}_n \text{base}^\text{place} where place \text{place} is zero-indexed from the right. The base is a positive integer no greater than 36. Therefore, the answer is an integer between and including 1 and 36.

More than one letter may represent a value. A given letter may not represent more than one value.

dichlorodiphenyltrichloroethane = dimethylglyoxime + actinium + vitamin

The leading value position of each number is nonzero.


The answer is 1.

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1 solution

A 31 letter word equals a 16 letter word plus a 8 letter word plus a 7 letter word. Each letter represents a weight of 1 and the base is 1. The base has to be small because of the length of the sum.

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