Letter Substitutions – 10
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 S, E, N, D, M, O, R, and Y to make this puzzle work.
EXPLORATION: Make some letter substitution puzzles for your friends to solve.
Notes
THE CHALLENGE
Because carries when adding two digits, plus a possible carry, are at most 1, the first thing to notice is that M must be 1.
Now that M is 1, look at S + 1 + (possible carry) = 1O on the left side of the puzzle. S + 1 + (possible carry) cannot be more than 11, and since letters cannot repeat another letter’s value, O must be 0.
Our puzzle now looks like this:
Because E + 0 = N, there must be a carry into that column and N must be one more than E. Also, that column does not produce a carry into the next column. This means S + 1 = 10, so S = 9.
With N being one more than E, and N + R + (possible carry) = 1E, this forces R = 8 and there is indeed a carry into that column.
Our puzzle now looks like this:
At this point there is nothing clever to do other than look at possibilities while remembering that E and N are consecutive numbers. The only way D + E = 1Y without duplicating values is for D = 7, E = 5, Y = 2, and N = 6.
At last we have the solution:
Notice how helpful it is to update the puzzle each time we determine the value of some new letters.