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wu :: forums    riddles    easy (Moderators: Grimbal, Icarus, Eigenray, william wu, ThudnBlunder, SMQ, towr)    7^1000 « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: 7^1000  (Read 597 times) codpro880 Junior Member Teachers strike, students hurt. English...     Gender: Posts: 89 7^1000   « on: Feb 26th, 2009, 11:44am » Quote Modify What is the number in the units place in 7^1000? Why? IP Logged You miss 100% of the shots you never take. pex Uberpuzzler     Gender: Posts: 880 Re: 7^1000   « Reply #1 on: Feb 26th, 2009, 12:03pm » Quote Modify Well, 74 = 1 (mod 10), so 71000 = 1250 = 1 (mod 10), right? IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: 7^1000   « Reply #2 on: Feb 26th, 2009, 12:04pm » Quote Modify A similar thread: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_eas y;action=display;num=1210461451 IP Logged Wikipedia, Google, Mathworld, Integer sequence DB codpro880 Junior Member Teachers strike, students hurt. English...     Gender: Posts: 89 Re: 7^1000   « Reply #3 on: Feb 26th, 2009, 5:31pm » Quote Modify Yes, 1 is the correct answer. I don't understand the mod stuff though :/. I need more schooling.   The way I solved the problem was by noticing that the powers of seven repeat the digits in the unit place in a pattern.   7^1=7 7^2=49 7^3=343 7^4=2401 7^5=16807 7^6=117649 etc. IP Logged You miss 100% of the shots you never take. pex Uberpuzzler     Gender: Posts: 880 Re: 7^1000   « Reply #4 on: Feb 26th, 2009, 10:51pm » Quote Modify on Feb 26th, 2009, 5:31pm, codpro880 wrote: I don't understand the mod stuff though :/ http://en.wikipedia.org/wiki/Modular_arithmetic is a good place to start. (Please note that officially, I used the "=" sign inappropriately; it should be something like "=".) IP Logged Hippo Uberpuzzler     Gender: Posts: 919 Re: 7^1000   « Reply #5 on: Mar 2nd, 2009, 8:10am » Quote Modify on Feb 26th, 2009, 10:51pm, pex wrote: I used the "=" sign inappropriately; it should be something like "=".) IP Logged codpro880 Junior Member Teachers strike, students hurt. English...     Gender: Posts: 89 Re: 7^1000   « Reply #6 on: Mar 2nd, 2009, 11:08am » Quote Modify So it's kind of like using different number bases except you go in a circle? IP Logged You miss 100% of the shots you never take. towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: 7^1000   « Reply #7 on: Mar 2nd, 2009, 11:31am » Quote Modify on Mar 2nd, 2009, 11:08am, codpro880 wrote: So it's kind of like using different number bases except you go in a circle? Yes, that's a good way to look at it. Just like using a clock, also. Add 24 hours and you get the same time again. IP Logged Wikipedia, Google, Mathworld, Integer sequence DB codpro880 Junior Member Teachers strike, students hurt. English...     Gender: Posts: 89 Re: 7^1000   « Reply #8 on: Mar 2nd, 2009, 3:53pm » Quote Modify on Feb 26th, 2009, 12:03pm, pex wrote: Well, 74 = 1 (mod 10), so 71000 = 1250 = 1 (mod 10), right?   I still don't get pex's logic   « Last Edit: Mar 2nd, 2009, 3:56pm by codpro880 » IP Logged You miss 100% of the shots you never take. River Phoenix Junior Member     Gender: Posts: 125 Re: 7^1000   « Reply #9 on: Mar 2nd, 2009, 5:16pm » Quote Modify on Mar 2nd, 2009, 3:53pm, codpro880 wrote:   I still don't get pex's logic     multiplication still works in a modulus number system, it just loops around. so since 7^4 = 1 (mod 10), therefore 7^8 = 1 * 1 = 1 (mod 10), etc. 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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