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wu :: forums    riddles    medium (Moderators: william wu, Icarus, Grimbal, Eigenray, ThudnBlunder, SMQ, towr)    Tough question « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Tough question  (Read 877 times) Polymath101 Newbie     Posts: 12 Tough question   « on: Apr 26th, 2009, 8:07pm » Quote Modify Suppose an octahedron consists of twelve rods all of equal length and forming eight equilateral triangles -- the eight sides of the octahedron. If any three of the rods are painted white and the rest black, how many distinct patterns are possible? IP Logged Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Tough question   « Reply #1 on: Apr 27th, 2009, 12:41am » Quote Modify Do you count mirroring as distinct patterns?   IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Tough question   « Reply #2 on: Apr 27th, 2009, 7:25am » Quote Modify Let's see if I can get it right for once 7 if mirroring doesn't count as distinct, 11 if it does. IP Logged Wikipedia, Google, Mathworld, Integer sequence DB Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Tough question   « Reply #3 on: Apr 28th, 2009, 9:56am » Quote Modify Hint:  It should be the same as for the cube. IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Tough question   « Reply #4 on: Apr 28th, 2009, 10:26am » Quote Modify on Apr 28th, 2009, 9:56am, Grimbal wrote: Hint:  It should be the same as for the cube. You mean the same as in the problem with the cube and four lights on the corners? Or the same as if we had a cube here? IP Logged Wikipedia, Google, Mathworld, Integer sequence DB Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Tough question   « Reply #5 on: Apr 28th, 2009, 10:22pm » Quote Modify In the sense of: paint 3 edges of a cube. IP Logged Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Tough question   « Reply #6 on: Apr 29th, 2009, 6:32am » Quote Modify Anyway, I find 9 or 13 depending on whether mirror images are distinct IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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