1998 AHSME Problems/Problem 1
Problem 1
Each of the sides of five congruent rectangles is labeled with an integer. In rectangle A, . In rectangle B, . In rectangle C, . In rectangle D, . In rectangle E, . These five rectangles are placed, without rotating or reflecting, in position as below. Which of the rectangle is the top leftmost one?
Solution
Looking at the list of and values that must match up left-to-right, we have . Looking for digits that only appear once, we see that , , , and cannot match up to other digits, and thus must appear on the ends. and only appear on the left, and thus their respective blocks and must appear on the left. Similarly, and only appear on the right, and thus their blocks and must appear on the right-most block of their row. Therefore, , the only block without a unique digit, must be the top-center block.
Now that we have placed one block, , we can only place block to the left of , and block to the right of . Thus, is the right answer.
Completing the puzzle, the top boxes read , while the bottom two boxes read .
See Also
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