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   THE LAST 1000 DIGITS: Puzzle Extension

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Topic: THE LAST 1000 DIGITS: Puzzle Extension (Read 719 times)

K Sengupta
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THE LAST 1000 DIGITS: Puzzle Extension
« on: May 27^th, 2006, 10:38pm »

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This refers to “THE LAST 1000 DIGITS” ( http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_har d;action=display;num=1133282207) which was contributed by pcbouhid.

How can the solution to the above problem be modified to determine the last 10,000 digits of the number

M = 1 + 40 + 40^2 + 40^3 + …………+ 40^9999?

« Last Edit: May 27^th, 2006, 10:41pm by K Sengupta »

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JocK
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Re: THE LAST 1000 DIGITS: Puzzle Extension
« Reply #1 on: May 28^th, 2006, 2:22am »

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M = (40^10,000 - 1)/(40 - 1)

M = ...999999999999999999 * 0.025641025641...

So, the last 1000 digits are just a repitition of the string "025641".

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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.

x^y - y = x⁵ - y⁴ - y³ = 20; x>0, y>0.

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