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wu :: forums    riddles    medium (Moderators: Grimbal, SMQ, Icarus, Eigenray, towr, ThudnBlunder, william wu)    first four digits of n^1,000,000 « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: first four digits of n^1,000,000  (Read 487 times) gkwal Newbie     Posts: 25 first four digits of n^1,000,000   « on: Jul 16th, 2007, 9:24pm » Quote Modify Find a positive integer n<10,000,000 such that the first four digits (in the decimal expansion) of n^1,000,000 are all different. The problem should be solved in your head!! IP Logged ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: first four digits of n^1,000,000   « Reply #1 on: Jul 17th, 2007, 9:29am » Quote Modify Considering one definition of e, 1,000,001 should do it. « Last Edit: Jul 18th, 2007, 3:30am by ThudnBlunder » IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Barukh Uberpuzzler     Gender: Posts: 2276 Re: first four digits of n^1,000,000   « Reply #2 on: Jul 17th, 2007, 10:16pm » Quote Modify Very elegant, ThudanBlunder!     Will 999999 also do? IP Logged Sameer Uberpuzzler Pie = pi * e     Gender: Posts: 1261 Re: first four digits of n^1,000,000   « Reply #3 on: Jul 17th, 2007, 10:30pm » Quote Modify I know it's late at night but I don't get it..     (1,000,001) ^ 1,000,000 (1 + 1,000,000) ^ 1,000,000 (1 + x) ^ x   Shouldn't it be (1 + 1/x) ^ x? IP Logged "Obvious" is the most dangerous word in mathematics. --Bell, Eric Temple Proof is an idol before which the mathematician tortures himself. Sir Arthur Eddington, quoted in Bridges to Infinity Barukh Uberpuzzler     Gender: Posts: 2276 Re: first four digits of n^1,000,000   « Reply #4 on: Jul 17th, 2007, 10:45pm » Quote Modify on Jul 17th, 2007, 10:30pm, Sameer wrote: I know it's late at night but I don't get it..     (1,000,001) ^ 1,000,000 (1 + 1,000,000) ^ 1,000,000 (1 + x) ^ x   Shouldn't it be (1 + 1/x) ^ x?   (1 + 1,000,000) ^ 1,000,000 = [1,000,000 * (1+ 1/1,000,000)] ^ 1,000,000 ~  1,000,000 ^ 1,000,000 * e IP Logged Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: first four digits of n^1,000,000   « Reply #5 on: Jul 18th, 2007, 12:07am » Quote Modify Out of curiosity, I tried numerically: 2^1M starts with 9900... 3^1M starts with 1797... 4^1M starts with 9802...   but I could hardly do that in my head.   IP Logged ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: first four digits of n^1,000,000   « Reply #6 on: Jul 18th, 2007, 4:36am » Quote Modify on Jul 17th, 2007, 10:16pm, Barukh wrote: Will [hide][/hide] also do? Yes, I was intending to add that we don't need n < 10 million as 1/e also works, but you have beaten me to it. IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. 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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