Post #2712474
2026-02-28 05:29 UTC
@divbyzero@mathstodon.xyz reminds me of the Martin Gardner problem where you drill though a sphere. If the length of the hole ends up at six inches, what is the volume of the remaining material? I won’t spoil it, but I always found the simplest way to the solution pretty enjoyable.
Replies (1)
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@rreusser@mathstodon.xyz 2026-02-28 05:54
@divbyzero@mathstodon.xyz oh! I should have scrolled down farther. Then I’ll spoil it and add that what I liked about it is that knowledge that it’s a brain-teaser can help you solve it. It’s not really a brain teaser unless the solution is interesting since Martin Gardner probably isn’t going to lob calculus questions at you, so we can guess that the solution is constant, and if there’s no dependence on the particular geometry, the hole might as well have radius zero, leaving a sphere, which trivially has volume 36pi, which happens to be correct in general!