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wu :: forums    riddles    easy (Moderators: Eigenray, Icarus, SMQ, Grimbal, ThudnBlunder, towr, william wu)    Electrical switches « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Electrical switches  (Read 442 times) Altamira_64 Junior Member     Posts: 116 Electrical switches   « on: Jan 7th, 2016, 1:34am » Quote Modify We have a set of 9 ON-OFF switches on an electrical board, initially all of them at the OFF position. What is the minimum number of moves to put them all at the ON position, if we must switch exactly 5 of them at each move? Same question but for 6 switches in each move? IP Logged rmsgrey Uberpuzzler     Gender: Posts: 2872 Re: Electrical switches   « Reply #1 on: Jan 7th, 2016, 10:11am » Quote Modify 5 at a time: 3 moves hidden: Parity considerations say it must be an odd number of moves. You need a total of 9+2n switchings, for n non-negative, so the minimum is 3 moves. It's easy to find solutions that work in 3 moves - eg 12345, 12367, 12389   6 at a time: !! moves hidden: You need a total of 9+2n switchings, which is odd, but each move makes an even number of switchings. Since there are no numbers which are both odd and even, parity considerations mean it can't be done (at least not with a finite number of moves) IP Logged Altamira_64 Junior Member     Posts: 116 Re: Electrical switches   « Reply #2 on: Jan 7th, 2016, 12:24pm » Quote Modify Excellent! How do you deduce the 9+2n condition? IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Electrical switches   « Reply #3 on: Jan 7th, 2016, 12:37pm » Quote Modify You need to turn on a switch 9 times, and any more switching needs to cancel out so must be even. « Last Edit: Jan 7th, 2016, 12:38pm by towr » IP Logged Wikipedia, Google, Mathworld, Integer sequence DB rmsgrey Uberpuzzler     Gender: Posts: 2872 Re: Electrical switches   « Reply #4 on: Jan 8th, 2016, 1:18pm » Quote Modify on Jan 7th, 2016, 12:24pm, Altamira_64 wrote: Excellent! How do you deduce the 9+2n condition?   You need 9 more "on"s than "off"s. n offs plus (n+9) ons makes 2n+9 total switchings. 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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