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 Evaluate this remainder (Posted on 2008-08-13)
What is the remainder when you divide 299 by 99?

 See The Solution Submitted by pcbouhid Rating: 4.0000 (1 votes)

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 re: Rereading (solution; spoiler) | Comment 2 of 6 |
(In reply to Rereading by brianjn)

If one starts with 2^0 = 1, and keeps doubling, and, when the result exceeds 98 subtracting 99, and keeps track of the power (adding 1 each time), you get the series:

`  0   1  1   2  2   4  3   8  4  16  5  32  6  64  7  29  8  58  9  17 10  34 11  68 12  37 13  74 14  49 15  98 16  97 17  95 18  91 19  83 20  67 21  35 22  70 23  41 24  82 25  65 26  31 27  62 28  25 29  50 30   1 `

From there on, this will repeat, so the cycle length is 30.

We want the 99th power of 2, so we can subtract 30*3=90 from the 99, and use the 9th power of 2, which is 17.

This is indeed the 2^4 + 1 given by brianjn.

 Posted by Charlie on 2008-08-13 11:14:51
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