(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.
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Posted by Charlie
on 2008-08-13 11:14:51 |
re: Rereading (solution; spoiler)
