Letter Substitutions – 4
Rules
- A letter represents a digit from 0 to 9, and has the same value throughout a single puzzle.
- No number can start with the digit 0.
- Within a puzzle, different letters must have different values.
THE CHALLENGE
Find the value of A, B, C, D, and E in these puzzles.
EXPLORATION
Make some letter substitution puzzles for your friends to solve.
Notes
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THE CHALLENGE
A + BB = C7: Adding A forces a carry, so C must be one more than B. A + B is 17, and the two numbers are one apart, so this must be 9 + 8 = 17.
The answer is 9 + 88 = 97.
D + ED = DE: Notice that D + D ends in E and has a carry. That is, D + D = 1E. Also, because of the carry to the tens place, D must be one more than E. List out the possibilities for D + D = 1E:
5 + 5 = 10, 6 + 6 = 12, 7 + 7 = 14, 8 + 8 = 16, 9 + 9 = 18.
The only one of these possibilities that fits the requirements is when D = 9 and E = 8.
The answer is: 9 + 89 = 98.