12
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This puzzle is based off the What is a Word™, What is a Phrase™ and What is a Number™ series started by JLee.

If a number conforms to a certain rule, I call it a CB Number™. Use the following examples to find the rule:

CB Numbers™ and Non-CB Numbers™

Here is a CSV:

CB Numbers™,Non-CB Numbers™
383,384
1412,1214
7557,8557
49537,43579
84286,86420
310222,420333
629218,639318
1234511,5432111
4762129,4763239
22222530,33333520
63655555,36355555
89899898,89898989

The puzzle relies on the series' inbuilt assumption, that each number can be tested for whether it is a CB Number™ own its own. In particular, a number's relationship to other numbers in the sequence is irrelevant.

These are not the only examples of CB Numbers™, more can be found.

The only reason the Non-CB Numbers™ are not in ascending order is because I have tried to make them look similar to the corresponding CB Numbers™ to their left. Note that this doesn't change the puzzle.

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  • $\begingroup$ CB Numbers™ aren't reliant on an obscure property of numbers like my previous question on weird numbers. $\endgroup$ – boboquack Oct 27 '16 at 21:10
  • $\begingroup$ are the letter's 'CB' significant, or are they arbitrary? $\endgroup$ – Pat Oct 27 '16 at 21:32
  • $\begingroup$ If they're arbitrary, I think they'd be the first puzzle of this sort in which the name had no significance at all. $\endgroup$ – Gareth McCaughan Oct 27 '16 at 21:39
  • $\begingroup$ @Pat They aren't arbitrary - they are of some significance, though they probably won't allow you to easily solve the puzzle. More that if you solve the puzzle in the way I intended, you would have a second point of conformation. $\endgroup$ – boboquack Oct 27 '16 at 21:46
14
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CB Numbers are numbers that

If you treat each digit as weights, the whole number balances on the midpoint of the scale.

For example,

in the number 1412, let us visualise as 1-4^1-2 where ^ indicates the midpoint. It can be observed that the distance-to-center of an outer digit is 3 times that of the inner digit.

We have,

the sum of weight times distance-to-center (left) = 1*3 + 4*1 = 7
the sum of weight times distance-to-center (right) = 1*1 + 2*3 = 7
Hence, 1412 balances on the midpoint.

CB probably stands for

Centrally balanced.

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