Cryptarithmetic

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Cryptarithmetic puzzles are arithmetic problems made of letters instead of numbers. The goal is to replace each letter with a single, unique digit in order to make the arithmetic work out correctly. Here are some I have invented.

English Bad, Math Good

  1. Solve the cryptarithmetic in base six: TO + TO = FOR.
  2. Solve the cryptarithmetic in base six: TOO + TOO = FOR. Now try it in base seven.
  3. Prove that there are no solutions to the cryptarithmetic in ANY base: WON + WON = TOO.