perplexus.info :: Numbers : All Combos 3

All Combos 3 (Posted on 2024-05-14)

A positive integer N contains each 2-digit combination exactly once:
00, 01, ..., 99.

(A) What is the smallest number of digits N could have?
(B) What is the largest number of digits N could have?
(C) What is the smallest possible value of N?
(D) What is the largest possible value of N?

(no leading zeros)

No Solution Yet Submitted by Larry

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Parts A and B (spoiler)

| Comment 2 of 5 |

A number with N digits has N-1 2 digit combinations, not necessarily distinct. Therefore, a number with 100 combinations exactly once must have exactly 101 digits, no more and no less.

This does not guarantee the existence of such a number. But if it exists, it must have 101 digits.

Posted by Steve Herman on 2024-05-15 06:32:51

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