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 A Bit of a Problem (Posted on 2004-12-07)
Find the pattern of the following sequence and determine the next few terms:
`2, 10, 12, 38, 42, 52, 56, 142, 150, 170`

 See The Solution Submitted by DJ Rating: 4.0000 (2 votes)

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 Solution (spoiler) | Comment 2 of 17 |

I was making no progress on this until I read the title.  The word "bit" was the clue.

If the numbers are put in binary form, you see a series of binary numbers with an even number of digits, such that the 1st n/2 digits and the last n/2 digits are figured differently.  The first half of the digits are the digits you would get, in order, by just counting in binary.  To figure the second half of the digits, count backwards in binary, but with the digits reversed.  Within each group based on the number of digits, the countdown for the second half ends at zero.

The second column below is the binary for each number in the series;  the third column is the decimal equivalent for each half of the binary digits with a comma between.  Remember the binary digits are reversed for the second half.

2:     10                1,0
10:   1010             2,1
12:   1100             3,0
38:   100110          4,3
42:   101010          5,2
52:   110100          6,1
56:   111000          7,0
142: 10001110       8,7
150: 10010110       9,6
170: 10101010       10,5
178: 10110010       11,4
204: 11001100       12,3

 Posted by Larry on 2004-12-07 15:20:35

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