Simpsons Cryptogram
For the above cryptogram, each letter represent a distinct non-negative single digit integer, find the value of the 5-digit integer, .
The answer is 15843.
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1 solution
Number the columns as follows: 12345
memo
+ from
homer
We note that O + M = R (column 5) and also O + M = E, (column 4) so column e must generate a carry of 1, and E = R + 1. Then from column 3, E + R + 1 = M (column 4 generates a carry also) and M = R + 1 + R + 1 = 2 R + 2.
So we have candidates for R E M as follows R E M 0 1 2 1 2 4 2 3 6 3 4 8 4 5 0 5 6 2 6 7 4 7 8 6 8 9 8 - eliminated by duplication 9 0 0 - eliminated by duplication
R - M = O, so we add a column for O
R E M O 0 1 2 8 1 2 4 7 2 3 6 6 - eliminated by duplication 3 4 8 5 4 5 0 4 - eliminated by duplication 5 6 2 3 6 7 4 2 7 8 6 1
We add ( ) which would be the carry from E + R + 1 = M, either 1 or 0, and F from M + F + carry ? = O R E M O ( ) F 0 1 2 8 (0) 6 1 2 4 7 (0) 3 3 4 8 5 (0) 7 5 6 2 3 (1) 0 6 7 4 2 (1) 7 - eliminated by duplication 7 8 6 1 (1) 4
In order to create the H in HOMER, M + F + carry ? must itself generate a carry R E M O (*) F 0 1 2 8 (0) 6 - elim, no carry out 1 2 4 7 (0) 3 - elim, no carry out 3 4 8 5 (0) 7 5 6 2 3 (1) 0 - elim, no carry out 7 8 6 1 (1) 4
That leaves R E M O (*) F 3 4 8 5 (0) 7 7 8 6 1 (1) 4 Since H must then be 1, the second row is eliminated and the solution is R E M O F H 3 4 8 5 7 1
MEMO 8485 +FROM 7358
HOMER 15843