The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

   

More Money

  SEND
+ MORE
------
MONEY
This cryptogram is amusing in that it spells out a meaningful message and has a unique solution. Deciphering the solution takes some persistent logical reasoning, although inspired guesswork can speed up the process.

The obvious initial assumption is that M equals 1. From the fact that SEND #+ MORE is greater than 9,999 we can conclude that S is either 8 or 9, because S + 1 (or 2, if there was a carry from the previous column) is greater than 9. Knowing this yields an upper limit for O; it must be either 0 or 1. Since M is 1, O must be 0. The code now looks like this:

  SEND
+ 10RE
------
 10NEY
The same logic gives us a value for S: if S is 8, then E plus zero is greater than 10 and N is less than 2. (For S to be 8, there must have been a carry) However, N is not less than 2, because all lower values are accounted for. Therefore S is 9. Knowing that there was a carry tells us that E equals N - 1. Looking at the middle two columns we see that EN plus R, plus a possible carry, equals NE. R must therefore be equal 8 or 9, depending upon the carry. Seeing that 9 is taken, R must be 8:

Looking at the one's column (D and E), we know there was a carry from this column, so D plus E is greater than 11 (10 and 11 being ruled out because they end with 0 and 1). Furthermore, 8 and 9 are accounted for, so D and E could be at most 6 and 7 in either combination. We also can place a minimum value at 5 for either one, if the other is 7. We also know that E cannot be 7, since it is one less than N. This means D cannot be 5. So E can be either 5 or 6.

Assume that E is 6; D must be greater than 5, and less than 8. Six is taken by E (in our assumption) leaving D equal to 7. But if E is 6, N must be 7. So from the contradiction, we know is not 6, therefore it is 5.

This makes N equal to 6, D equal to 7 and Y equal to 2. The "message" translates to:

  9567
+ 1085
------
 10652

The student needed $10,652. We know this because the method used to solve the problem eliminated the possibility of alternate solutions. So SEND + MORE = MONEY as a monoalphabetic cipher has a unique solution.

Updated 3/27/1999:

Some people have pointed out that there is an alternate solution if a number can begin with zero. True, but why waste the extra character? I believe (could be wrong) telegrams are by the character, not word.

3.42 stars. Votes are updated daily.


On a scale of 1 to 5, 1 being among your least favorite, 5 being among your most favorite, how would you rate this puzzle?

1 2 3 4 5

Copyright © 1996-2024 Wx3, All Rights Reserved.