The Game of Boxes

The game of boxes is a great way to practice addition! In this game you keep placing consecutive numbers into the boxes until you get stuck. The game's one rule: you cannot place a number in a box if the box already contains two numbers that add up to it. For instance, you cannot place a 10 in a box containing a 4 and a 6, or place a 7 in a box containing a 2 and a 5. How high can you get?

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DETAILS

The game of boxes is based on a problem posed in 1916 by the mathematician I. Schur, which remains unsolved to this day. In the case of two boxes, the maximum number is 8, and with three boxes the maximum number is 23. No one knows how high you can go with five boxes!
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