Solution #82: Take a Letter

X=4, Y=9 and Z=5.

In the middle column, adding Y to Z gives a digit of Z. This means Y must be either a 0 or a 9. (It can be a 9 if the addition in the far right column causes carrying a 1 into the middle column.) Since Y is the first digit in the number on the bottom, it cannot be a zero. So, Y=9.

The two X's in the left column plus a possible 1 carried from the middle column must add up to Y, which is 9. Since 9 is odd, a 1 must have been carried over from the middle column, leaving X+X=8. So, X=4.

The value of Z can be determined from the right column: Since Y=9 and X=4, Z must be 5 because it is the only digit that can be added to 9 that puts a 4 in the one's place (9+5=14).

Source: Fixx, James F
Categories: Puzzle, Arithmetic, Addition, Reasoning
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