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wu :: forums    riddles    easy (Moderators: towr, Icarus, ThudnBlunder, Eigenray, Grimbal, william wu, SMQ)    Easy: Inverse sum of squares « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Easy: Inverse sum of squares  (Read 6592 times) Qwerty Newbie     Posts: 1 Easy: Inverse sum of squares   « on: Mar 21st, 2003, 8:24am » Quote Modify By adding inverses of perfect squares (e.g. 1/4, 1/9, 1/16, etc...) to each other, create a summation that equals exactly 1/2.   Constraints: You may not repeat any value. You may not use the inverse of any values greater than 100^2. IP Logged prince Newbie     Posts: 49 Re: Easy: Inverse sum of squares   « Reply #1 on: Mar 21st, 2003, 1:17pm » Quote Modify Using your max allowable value as a hint, I came up with the following: 1/4 + 1/9 + 1/16 + 1/25 + 1/36 + 1/225 + 1/400 + 1/900 + 1/3600 + 1/5625 + 1/10000   Is there more than 1 solution? IP Logged SWF Uberpuzzler     Posts: 879 Re: Easy: Inverse sum of squares   « Reply #2 on: Mar 27th, 2003, 5:07pm » Quote Modify on Mar 21st, 2003, 1:17pm, prince wrote: Is there more than 1 solution?   Yes, there are many solutions.  Below are seven groups of integers whose sum of reciprocal squares is 0.5: 2 3 4 5 7 12 15 20 28 35 2 3 4 5 7 12 13 28 35 39 52 2 3 4 5 7 10 20 28 30 35 60 2 3 4 5 7 9 28 35 36 45 60 2 3 4 5 6 15 21 28 60 70 84 2 3 4 5 6 18 21 24 30 60 87 2 3 4 5 6 12 36 45 60 90 2 3 4 5 6 15 20 36 45 60 90 Note that there are 8 groups above, but only 7 are correct. Basic arithmetic problem:  which one is bogus? IP Logged cho Guest Re: Easy: Inverse sum of squares   « Reply #3 on: Mar 27th, 2003, 6:10pm » Quote Modify Remove The bogus one kind of stands out if you notice what the numbers in any group have in common. IP Logged SWF Uberpuzzler     Posts: 879 Re: Easy: Inverse sum of squares   « Reply #4 on: Apr 16th, 2003, 5:46pm » Quote Modify What do you mean, cho?  The common thing among 7 of them is that the sum of their reciprocals is 1/2.  Do you mean something else? IP Logged cho Guest Re: Easy: Inverse sum of squares   « Reply #5 on: Apr 16th, 2003, 6:18pm » Quote Modify Remove What they have in common is factors. In the valid answers there is no factor that occurs only in one number. The bogus answer has 2 numbers with unmatched factors. 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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