### Puzzlepedia^{™} Cryptography Brain Teasers

# Crypto-Math

A simple arithmetic problem has the numbers replaced with letters.

In a Crypto-Math (also called Verbal Arithmetic, Alphametics or Crypto-Number) puzzle, a simple arithmetic problem has had the numbers replaced with letters. Your job is to reverse the process and figure out which number make the arithmetic problem correct. Typically, each number is represented by only one letter and in good puzzles, there is only one solution.

Example:

The method for solving this example is as follows:

- The largest 5 digit number that can be made from two 4 digit number is 9999+9999=19998, so M=1.
- With M=1, the largest sum we can make now is 9999+1999=11998. This means that O must be either a 1 or 0. We have already used 1 so O=0.
- Looking at the third column of numbers, we know that E+0 cannot have a sum greater than 9, therefore there is no carryover into column two and S+1 must equal 10. So S=9.
- Looking at the third column of numbers again, we know that E+0≠N so there must be a carryover from column four which means that E+1=N. Using this equation and looking at column four, we can see that R must be either 9 or 8 with a carryover from column five. We have already used 9, so R=8.
- We already know that N=E+1, so looking at the unused numbers we have these possibilities for N/E: (7/6),(6/5),(5/4),(4/3),(3/2). Looking at the right most column, we know that D+E=Y+10 or D=Y+10-E and we know that Y must be 2 or greater because the number 1 is already used. Now we try the possible values for E in this equation. If E=2 then D must by greater than 9, so its out. IF E=3 then D=9 which is already used, so thats out. Continue trying each possibility and you'll find the only possible answer. E=5.
- We already know that N=E+1 so N=6.
- All thats left is to solve D and Y and with the remaining numbers there is only one possibility: D=7 and Y=2.

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