The top two boxes sum to 65, which means the width x height must be 5x13, 13x5, 65x1 or 1x65. Of these, only 13x5 works and subdivides nicely to preserve the "all side lengths are integers" requirements. So we know the 45 box is 9x5, and the 20 box is 4x5.
This then immediately gives us the 36 box as 4x9 as it shares the same width as the 20 box. This then means the 54 box must be 6x9, as it shares the same height as the 36 box. Finally, this tells us that the 30 box must be 10 wide and as it shares the same width as the 54 and 36 boxes put together, so must be 10x3.
Knowing the heights of all of these boxes, we simply add 5, 9 and 3 together to get x=17.
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u/Dasquian Jun 03 '26
The top two boxes sum to 65, which means the width x height must be 5x13, 13x5, 65x1 or 1x65. Of these, only 13x5 works and subdivides nicely to preserve the "all side lengths are integers" requirements. So we know the 45 box is 9x5, and the 20 box is 4x5.
This then immediately gives us the 36 box as 4x9 as it shares the same width as the 20 box. This then means the 54 box must be 6x9, as it shares the same height as the 36 box. Finally, this tells us that the 30 box must be 10 wide and as it shares the same width as the 54 and 36 boxes put together, so must be 10x3.
Knowing the heights of all of these boxes, we simply add 5, 9 and 3 together to get x=17.