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Evaluate this remainder (Posted on 2008-08-13) Difficulty: 2 of 5
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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Solution 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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