Letter Substitutions – 2
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 C, D, E, F, G, and H in these puzzles.
EXPLORATION
Make some letter substitution puzzles for your friends to solve.
Notes
THE CHALLENGE
In problems with more letters, it is often helpful to rewrite the problem replacing each letter as you discover its value.
These problems involve an important insight about adding: if you add two single-digit numbers, including possibly a carry, the result cannot be larger than 19, so the carry is always either 0 or 1.
In the first problem, as a leading digit D cannot be 0, so it must be 1. C + 2 must be at least 10, so C is 8 or 9. If C is 9, then DE would be 11 – this would cause D and E to have the same value, which is not allowed. Therefore, C is 8, and the answer is: 8 + 2 = 10.
The second starts off the same way. F must be 1. The problem becomes 1 + G = 1H. The only way 1 + G can be 10 or higher is for G to be 9. The answer becomes: 1 + 9 = 10.
EXPLORATION
Here are three more letter substitution puzzles to play with.
J + J + K = K0: As a carry, K must be 1 or 2. If K is 1, then J + J + 1 is an odd number, which cannot end in 0. Therefore, K is 2. Now, J + J + 2 = 20 forces J to be 9. The answer is: 9 + 9 + 2 = 20.
L + L + L = M2: Three times L ends in 2 forces L to be 4 and M to be 1. The answer is: 4 + 4 + 4 = 12.
N + N + N = P4: Three times N ends in 4 forces N to be 8 and P to be 2. The answer is: 8 + 8 + 8 = 24.