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)
(In reply to
re(2): Parts A and B (spoiler) & small example by Jer)
To carry Jer's idea along, once any solution is found, the numerical digits could be replaced with letters A,B,...,J where A is the first digit, B is the next new digit and so on. I'm not sure if this "letter pattern" is unique, but I think it might be.
If the letters are to be replaced by numerical digits, there are 9 choices for A, 9 choices for B, 8 for C etc.
So I assume there are 9*9! solutions (per pattern and maybe there is only one pattern).
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Posted by Larry
on 2024-05-16 22:30:46 |
re(3): Parts A and B (spoiler) & small example
