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wu :: forums    riddles    hard (Moderators: william wu, Eigenray, SMQ, towr, Grimbal, ThudnBlunder, Icarus)    Cutting a cube « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Cutting a cube  (Read 3612 times) Benny Uberpuzzler     Gender: Posts: 1024 Cutting a cube   « on: Jan 31st, 2008, 9:03pm » Quote Modify If you cut a cube of material with 5 perfectly straight slices all the way through? What is the maximum amount of separate pieces you can create?   These links may help:   http://www.eskimo.com/~miyaguch/power.html   http://www.research.att.com/~njas/sequences/A000125     IP Logged If we want to understand our world — or how to change it — we must first understand the rational choices that shape it. towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Cutting a cube   « Reply #1 on: Feb 1st, 2008, 12:27am » Quote Modify Can you move the pieces between cuts?   Do you have to cut parallel to the sides of the cubes? IP Logged Wikipedia, Google, Mathworld, Integer sequence DB Benny Uberpuzzler     Gender: Posts: 1024 Re: Cutting a cube   « Reply #2 on: Feb 1st, 2008, 2:57am » Quote Modify This is what i did :   The maximal number of pieces into which "n" planes divide the space, is given by: (n^3 + 5n + 6)/6, so the answer to this question is 26.   What do u think? Do u agree with the solution? IP Logged If we want to understand our world — or how to change it — we must first understand the rational choices that shape it. ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Cutting a cube   « Reply #3 on: Feb 1st, 2008, 3:06am » Quote Modify on Feb 1st, 2008, 2:57am, BenVitale wrote: This is what i did : The maximal number of pieces into which "n" planes divide the space, is given by: (n^3 + 5n + 6)/6, so the answer to this question is 26. What do u think? Do u agree with the solution? (n^3 + 5n + 6)/6 is a deus ex machina formula, not a solution.   IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Cutting a cube   « Reply #4 on: Feb 1st, 2008, 6:41am » Quote Modify I can get 32 if (and only if) I can move the pieces around for each planar cut. If you have to make cuts parallel to the sides of the cubes (without moving pieces around), I get 18. And 26 is a perfectly correct answer in the case you just divide the cube with random planes (without moving the pieces). IP Logged Wikipedia, Google, Mathworld, Integer sequence DB 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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