2017-11-08 17:39:50 +01:00
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A spider, **S**, sits in one corner of a cuboid room, measuring `6 by 5 by 3`,
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and a fly, **F**, sits in the opposite corner.
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By travelling on the surfaces of the room the shortest "straight line"
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distance from **S** to **F** is 10 and the path is shown on the diagram.
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2018-02-03 18:49:23 +01:00
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2017-11-08 17:39:50 +01:00
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However, there are up to three "shortest" path candidates for any given cuboid and
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the shortest route doesn't always have integer length.
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It can be shown that there are exactly `2060` distinct cuboids, ignoring rotations,
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with integer dimensions, up to a maximum size of `M by M by M`,
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for which the shortest route has integer length when `M = 100`.
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This is the least value of M for which the number of solutions first exceeds two thousand;
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the number of solutions when `M = 99` is `1975`.
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Find the least value of M such that the number of solutions first exceeds one million.
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