Print-It-Yourself Puzzles

Currently Playing: 37 Spike Caltrop - Can there be a caltrop with 5, 9, 17, 33 or 65 spikes?

Print it yourself at https://oskarvandeventer.nl/Print-It-Yourself/. 37-Spike Caltrop is a caltrop with, well, 37 spikes. Regular caltrops have four spikes in a tetrahedral configuration. This object always falls such that one spike is straight up, ready to puncture tires. One can easily design a six-spike caltrop based on the geometry of a pentagonal pyramid. It has the same property that there will always be one spike straight up, when it rests on a flat surface. Also 37-Spike Caltrop has this same property. There will always be a spike straight up. Conversely, one can point each of the spikes straight up, and the object can rest on a flat surface. There is a straightforward approach to make a caltrop with almost any number N, if either N-1 is odd, or N-1 is dividable by an odd number. This leaves out all N-1 that are a power of two. Hence, an open question is whether there exists caltrops with 5, 9, 17, 33 or 65 spikes. Copyright (c) 2025, M. Oskar van Deventer. Frequently Asked Question: http://oskarvandeventer.nl/FAQ.html Buy mass-produced Oskar puzzles at https://www.puzzlemaster.ca/browse/inventors/oskar/ (USA, CA) and https://www.sloyd.fi/brain-teasers/inventors-designers/oskar-van-deventer (EU) Buy exclusive 3D-printed Oskar puzzles at https://i.materialise.com/shop/designer/oskarpuzzle, https://www.chewiescustompuzzles.com/puzzleshop/oskars-puzzles