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wu :: forums    riddles    easy (Moderators: Grimbal, Icarus, towr, william wu, ThudnBlunder, Eigenray, SMQ)    Find the last digit(s) « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Find the last digit(s)  (Read 953 times) wonderful Full Member     Posts: 203 Find the last digit(s)   « on: May 10th, 2008, 4:17pm » Quote Modify 1. Find the last digit number of  2004^2005   2/ Find the last two digit numbers of  17^17^17   3. Find the last three digit numbers of 1993^1994^1995^...^10000   Have A Great Day! IP Logged Random Lack of Squiggily Lines Senior Riddler Everything before 7/1/2008 is now irrelevant.     Gender: Posts: 460 Re: Find the last digit(s)   « Reply #1 on: May 10th, 2008, 4:58pm » Quote Modify 1) uh, 6? 2) the last digit is 1. I guess « Last Edit: May 10th, 2008, 5:00pm by Random Lack of Squiggily Lines » IP Logged You can only believe i what you can prove, and since you have nothing proven to cmpare to, you can believe in nothing. I have ~50 posts to hack a "R" into a "D". Which one? black_death Newbie     Gender: Posts: 40 Re: Find the last digit(s)   « Reply #2 on: May 10th, 2008, 5:32pm » Quote Modify on May 10th, 2008, 4:17pm, wonderful wrote: 1. Find the last digit number of  2004^2005 odd powers of 4 should result in last digit of 4 IP Logged SMQ wu::riddles Moderator Uberpuzzler     Gender: Posts: 2084 Re: Find the last digit(s)   « Reply #3 on: May 12th, 2008, 7:15am » Quote Modify Using the results from this thread, we have:   1) 20042005 (mod 10) 41 (mod 10) = 4   2) 17^17^17 (mod 100) 17^[17^17 (mod 40)] (mod 100) 17^17 (mod 100) = 77   3) 1993^1994^1995^...^10000 (mod 1000)       993^[394^{75^[12^{13^[14^{7^[0^... (mod 4)] (mod 8)} mod 16)] (mod 32)} (mod 64)] (mod 160)} (mod 400)] (mod 1000)       993^[394^{75^[12^{13^[14^{7^0 (mod 8)} mod 16)] (mod 32)} (mod 64)] (mod 160)} (mod 400)] (mod 1000)       993^[394^{75^[12^{13^[14^9 mod 16)] (mod 32)} (mod 64)] (mod 160)} (mod 400)] (mod 1000)       993^[394^{75^[12^{13^0 (mod 32)} (mod 64)] (mod 160)} (mod 400)] (mod 1000)       993^[394^{75^[12^33 (mod 64)] (mod 160)} (mod 400)] (mod 1000)       993^[394^{75^64 (mod 160)} (mod 400)] (mod 1000)       993^[394^65 (mod 400)] (mod 1000)       993^224 (mod 1000) = 401   --SMQ « Last Edit: May 12th, 2008, 11:58am by SMQ » IP Logged --SMQ wonderful Full Member     Posts: 203 Re: Find the last digit(s)   « Reply #4 on: May 12th, 2008, 2:04pm » Quote Modify Excellent SMQ!   Have A Great Day! 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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