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For example

Not Accepted values: $4444$ (4444 is not a "pair"), $4040$, $4141$, $4440$ (444 is not a "pair").

Accepted values: $4400, 4401, 0440, 4404, 4004$

Digits may be $0-9$, not just 4 and 0 etc..

So far I've got ($1 - 10P4 - 10 $) which is (All - no repeating digits - all digits are the same). I've no idea how to go on with the other conditions. Perhaps my approach is wrong?

bg9848
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  • Could you elaborate it more? Your explanation is quite confusing. Also, using $ sign to write equations and numbers. – Aniruddha Deshmukh Jan 22 '18 at 05:39
  • I see $3$ pairs in $4444$. And is $3030$ a same pair? – Myridium Jan 22 '18 at 05:54
  • pair = 2 equal numbers 0-9 side by side. Must be one or two pairs. – bg9848 Jan 22 '18 at 05:56
  • So $4440$ is an accepted value then? Please be more precise in your question so it's easier to understand. – Myridium Jan 22 '18 at 06:01
  • Sorry I've no further explanation. The examples for accepted / not accepted is the best I've got. It really is a confusing question though. Also, the examples are not all of the possibilities. – bg9848 Jan 22 '18 at 06:05

1 Answers1

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Hint:

Six possible forms: $$aabc, \quad baac, \quad bcaa$$ $$aaab, \quad baaa$$ $$aaaa$$ where $a,b$ and $c$ are pairwise distinct.

For the first three forms, we have $(10\times 9 \times 8) \times 3$ choices.

For the second row, we have $(10 \times 9) \times 2$ choices.

For the third row, we have $10$ choices.

In total, we have $2350$ choices from above. There are a couple of forms remaining. Can you finish?

Myridium
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  • The last three are not ok. And aabb, abba and aaba would be in there too. Maybe more. But ur approach seems good. I do not know though. – bg9848 Jan 22 '18 at 06:33
  • @bg9848 - Sorry, you are right. Try extending my technique so that you get the correct answer. – Myridium Jan 22 '18 at 09:52
  • I think the accepted forms are $aabc$, $baac$, $bcaa$, $aaba$, $abaa$, $aabb$, and $baab$. – Barry Cipra Jan 22 '18 at 10:52