Can you arrange seven distinct points on a plane, so that of any three taken at random, at least two would...
geometry/seven.points New
New entry, edited from material collected for the archive and not yet in a released version.
Problem
Can you arrange seven distinct points on a plane, so that of any three taken at random, at least two would be exactly one unit apart? -- Don Quinsland <dquinsla@i84.net>
Show solution
That's a good puzzle. I know I enjoyed working on it! Spoiler in ROT13: Gb neenatr fvk fhpu cbvagf vf rnfl. Lbh whfg cynpr gurz ng gur pbearef bs gjb rdhvyngreny gevnatyrf, juvpu qba'g rira unir gb or pybfr gb rnpu bgure. Gur punyyratr vf gb neenatr gur gjb gevnatyrf naq n friragu cbvag, fb gung gur pbaqvgvbaf ner fgvyy fngvfsvrq. Fgneg ol qenjvat n pvepyr bs havg enqvhf. Cvpx gjb cbvagf ba gur pvephzsrerapr bs guvf pvepyr gung ner bar havg ncneg, cyhf n guveq cbvag, bhgfvqr bs gur pvepyr, fb nf gb sbez na rdhvyngreny gevnatyr jvgu fvqrf bs bar havg. Phg bhg guvf pvepyr-jvgu-nggnpurq-gevnatyr jvgu fpvffbef, znxr nabgure pbcl, naq phg vg bhg gbb. Cynpr gurz ba gbc bs rnpu bgure naq fgvpx n cva guebhtu gur pragref bs gur gjb pvepyrf. Abj ebgngr gur pvepyrf fb gung gur cebgehqvat cbvag bs bar bs gur nggnpurq gevnatyrf vf bar havg njnl sebz gur pbeerfcbaqvat cbvag bs gur bgure gevnatyr. Gur pbearef bs gur gjb gevnatyrf ner fvk bs gur erdhverq cbvagf, naq gur funerq pragre bs gur gjb pvepyrf vf gur friragu. Ab frg bs guerr cbvagf rkvfgf jurer nyy guerr ner frcnengrq ol n qvfgnapr qvssrerag guna bar havg. -- O. Realymink <o.realymink@anagrams.r.us> [ Editor: the spoiler is kept in ROT13 as posted (rotate each letter 13 places to read it). ]