问题：
E T W Q
+ F E F Q
= A W Q Q Q
解题过程：
E=7，W=4，F=6，T=2，Q=0，东路兵力是 7240，西路兵力是 6760，总兵力是 14000。细心分析，可以发现只能是 Q+Q=Q，而且 Q+Q=2Q，故 Q=0。同样，只能是 W+F=10，T+E+1=10，E+F+1=10+W。所以有三个式子：W+F=10（1）T+E=9（2）E+F=9+W（3）推出 2W=E+1，所以 E 是单数。另外 E+F>9，E>F，所以推算出 E=9 是错误的，E=7 是正确的。
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Welcome to cryptarithmetic puzzles! In these mathematical puzzles, each letter represents a unique digit from 0 to 9. Our goal is to find what digit each letter represents to make this addition equation valid. Notice the column structure - we have units, tens, hundreds, and thousands places. The carry operations between columns will be crucial for solving this puzzle systematically.
Now let's analyze the column patterns systematically. Looking at the rightmost column, we see Q plus Q equals Q. For this equation to work with single digits, we need to find when Q plus Q equals Q. Since Q plus Q equals 2Q, we need 2Q to equal Q. The only digit where this is true is zero, because 2 times 0 equals 0. Therefore, Q must equal 0. Let's substitute this value and see how it transforms our puzzle.
Now let's systematically analyze the carry operations with Q equals zero. Looking at the tens column, we have W plus F equals W. This would mean F equals zero, but we already know Q equals zero, and each letter must represent a unique digit. Therefore, W plus F must equal 10, creating a carry of 1. Moving to the hundreds column, T plus E plus the carry of 1 equals 10, so T plus E equals 9. Finally, in the thousands column, E plus F plus the carry equals 10 plus W, giving us E plus F equals 9 plus W. These three equations will be the key to solving our puzzle.
Now let's transform our column analysis into a solvable system of equations. We have three key equations: W plus F equals 10, T plus E equals 9, and E plus F equals 9 plus W. To find relationships between variables, let's substitute. From equation 1, we get F equals 10 minus W. Substituting this into equation 3: E plus 10 minus W equals 9 plus W. Simplifying: E equals 2W minus 1. This is a crucial insight - since E equals 2W minus 1, and 2W is always even, E must be odd!
Now let's apply additional constraints to find the specific solution. We need E plus F greater than 9 to generate a carry, E greater than F since E appears in the thousands place, E must be odd, and all digits must be unique. Let's test the odd values systematically. If E equals 9, then W equals 5 and F equals 5, but this violates the uniqueness constraint since W and F would be the same. If E equals 7, then W equals 4 and F equals 6. From T plus E equals 9, we get T equals 2. Let's verify: 7 plus 6 equals 13, which is greater than 9, check. 7 is greater than 6, check. All digits are unique, check. Therefore, our solution is E equals 7, W equals 4, F equals 6, T equals 2, and Q equals 0.