Cryptarithm

A cryptarithm is a mathematical puzzle where letters represent unique digits in an arithmetic equation. The goal is to find the digit-to-letter mapping that makes the equation valid.

How to Solve

1. Analyze the equation: Look at the structure of the addition/subtraction problem
2. Use the numeric example: The puzzle provides a solved numeric version to help you understand the letter-to-digit mapping
3. Apply logical constraints:
   • Each letter represents a unique digit (0-9)
   • Leading letters cannot be zero
   • Column-wise addition must hold with carries
4. Map letters to digits: Use the provided grid to assign digits to letters
5. Decode the message: Use your mapping to decode the number strings into words

Example

Given the cryptarithm:

  E A T
+ T H A T
---------
A P P L E

With the numeric example:

  8 1 9
+ 9 2 1 9
---------
1 0 0 3 8

Solution Process:

• From the numeric example: E=8, A=1, T=9, H=2, P=0, L=3
• Verify the addition: 819 + 9219 = 10038 ✓
• Decode the digit groups: 2 8 1 9 → H E A T, 9 2 8 → T H E, 0 3 1 9 8 → P L A T E
• Final answer: "HEAT THE PLATE"

Tips

• Start with the rightmost column and work leftward
• Pay attention to carries between columns
• Use the hint to verify your decoded message makes sense
• Remember that leading letters cannot be zero

Video Tutorial