Cryptarithm Rules: The 7 Rules You Need

A cryptarithm replaces digits with letters or symbols. The goal is to recover the digits while keeping the arithmetic correct.

1. One letter means one digit

If A = 4, every A in that puzzle is 4. Different letters normally represent different digits.

2. Leading letters are not zero

The first letter of a multi-digit number cannot be 0. Otherwise a three-digit word could secretly become a two-digit number.

3. Work column by column

Start at the units column and move left. Each column gives a small equation plus a possible carry.

The units column says B + D = F + 10×carry.

4. Carries are constraints

In addition of two digits, the carry to the next column is usually 0 or 1. That tiny fact can eliminate many candidates immediately.

5. Never guess when you can eliminate

Keep candidate digits for each letter. Cross out digits already used or made impossible by a column. A forced digit is safer than a lucky guess.

6. Check the whole equation

A locally valid column is not enough. Substitute every solved digit back into the complete arithmetic before declaring the puzzle solved.

7. Use contradictions

If a trial forces two letters to share a digit, creates an impossible carry, or makes a leading letter zero, reject that branch and return to the last certain step.

Educational note: these techniques are practice methods, not medical or cognitive-performance claims.