It all adds up

This puzzle may look like another plea from Des Wood for more cash to bolster the club's funds, but it isn't! It is actually one of the most famous puzzles of all-time. It was created by Henry Dudeney - a self taught mathematician from Mayfield in Sussex, and one of the world's greatest inventors of puzzles. It first appeared in the July 1924 issue of Strand Magazine.

The puzzle

   S E N D
 + M O R E
 M O N E Y

This is a correct addition sum in which each different letter stands for a different digit. What is the original sum?

The solution

   9 5 6 7
 + 1 0 8 5
 1 0 6 5 2

M=1 as the total of the column SM cannot be as high as 20. To make the S+1 column big enough to carry over to the next column S=8 or 9. In either case the letter O must stand for 0 as the S+1 column can only be 10 or 11 and it cannot be 1 as M=1. In column E+0 the total cannot be as high as 10, so there will be no 1 to carry over, so S=9. E+0 gives N so N=E+1 and the N+R total greater than 10. So N+R+1=E+10, so R=8 and 1 must be carried over from D+E. Column DE must total at least 12 since Y cannot be 1 or 0. The only digits left that can reach this high are 7+6 or 7+5. But one of these has to be E and N has to be E+1, so E=5, N=6 and D=7. This makes Y=2.

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