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2011 Powered Digits (Posted on 2011-03-25) Difficulty: 3 of 5
Find the first digit before and after the decimal point in the base ten expansion of (√2 + √3)2011.

For an extra challenge, solve this puzzle without using a computer program.

No Solution Yet Submitted by K Sengupta    
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re: The Broll guesses... | Comment 2 of 5 |
(In reply to The Broll guesses... by broll)

Why did you stop at  (a+b)^2000?
Your reasoning breaks down if you instead use a different large even power:

= (a+b)^2002*(a+b)^9

=(something huge)+0.9999999999........9*(a+b)^9

(a+b)^9= 30210.4301525

so the digits before and after the decimal point should be ...0.4...?

  Posted by Jer on 2011-03-25 14:28:25

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