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Ascending Hexadecimal Digits (Posted on 2016-09-15) Difficulty: 3 of 5
Determine the total number of values of a hexadecimal positive integer N such that:
N does not contain any leading zero, and:
N has at least two digits, and:
The digits of N are strictly ascending from left to right.

No Solution Yet Submitted by K Sengupta    
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Solution solution Comment 1 of 1
Since the numbers are strictly ascending, precluding duplicates and assuring exactly one representation for any set of digits present, we need only concern ourselves with combinations rather than permutations.

Again since they are ascending, the prohibition on leading zeros is a prohibition on zeros altogether.

Any of the 15 other digits, 1 through F, can either appear or not appear in the integer N, so initially we come up with 2^15. But this includes a no-digit "number" as well as 15 1-digit numbers, so the final answer is 2^15 - 16 = 32,752.

  Posted by Charlie on 2016-09-15 10:08:44
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