Letter Substitutions – 11
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 to make this puzzle work.
EXPLORATION
Make some letter substitution puzzles for others to solve.
Notes
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THE CHALLENGE
The key to solving this is to focus on A x E = E, 1E, 2E, or whatever is needed before the E. There are very few combinations of single digits that have this property. Note that A cannot be 0 or 1, and E cannot be 0. Here is the list of the possibilities, listing as A, E:
3, 5: 3 x 5 = 15
5, 1: 5 x 1 = 5
5, 3: 5 x 3 = 15
5, 7: 5 x 7 = 35
5, 9: 5 x 9 = 45
7, 5: 7 x 5 = 35
9, 5: 9 x 5 = 45
Once you have this list, it is quick work to see that A = 7 and E = 5 is the only one that works. This gives the solution A = 7, B = 9, C = 3, D = 6, and E = 5. The finished puzzle looks like this:
