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One counting problem

 
 
Wang Henry 的相片
One counting problem
由Wang Henry 發表於2025年 08月 5日(Tue) 17:20
 

How many six digit numbers are there that have exactly one pair of digits that differ by 5? Can anyone give me a hand? Thanks.

 
Admin ZIML的相片
Re: One counting problem
由Admin ZIML發表於2025年 08月 6日(Wed) 03:03
 

There are $5$ possible pairs: $(0,5)$, $(1,6)$, $(2,7)$, $(3,8)$, and $(4,9)$.  Only one of these pairs have both digits appear, non-repeating.  For each of the other pairs, only one digit can appear, repeating allowed. Also consider $0$ cannot be the first digit.

 
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