Enigma 166: Water storage
3 February 2014
Posted by on
From New Scientist #1311, 24th June 1982 [link]
This is a bird’s eye view of my present water store. I got 16 cuboids each 1′×1′, with lengths of 1′, 2′, …, 16′. I stacked them all on end on a level 4′×4′ base and glued them together in that position. As you can see the store’s capacity is 9 (cubic feet). My glue is strong enough to waterproof corner joints, e.g. between 4 and 7 or between 8 and 11. So 3 cu. ft. will stand on number 1, but any more will spill out over 4. And 6 cu. ft. will stand on number 2.
You will notice I could have achieved a bigger capacity with my 16 cuboids. In fact, I could have got 26 cu. ft. But I need something much bigger than that. So I am going to start again with a fresh supply of 64 cuboids, each 1′×1′ again of length 1′, 2′, 3′, …, 64′.
If I stack these on end on an 8′×8′ level base, so that they will hold as much water as possible when glued together, what will be the capacity in cubic feet? I don’t mind if the water is stored in one connected “tank” or (as with my present store) in more than one.