Brain Teasers
3 Consecutive Sums
Place a number in each of the following empty boxes so that the
sum of the numbers in any 3 consecutive boxes is 2013. What is the number that
should go in the box with the question mark?
Puzzle provided by Noetic Learning Math
Contest
Solution: 682.
To help illustrate the problem, we
will label a few boxes as shown below. Since the sum of the numbers in any 3
consecutive boxes is the same, 607 + A + B = A + B + C. Therefore, the number
in box C should be 607.
The sum of the numbers in any 3 consecutive
boxes is 2013, therefore we have
C + 724 + ? = 2013.
C is 607. So we have 607 + 724 + ? =
2013. Therefore, the box with the question mark should be 2013-607-724 = 682.
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