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  • If $2731$ has to appear in $x$, we should have $910$ in $V$
  • If $2731$ has to appear in $y$, we should have $546$ in $V$
  • If $2731$ has to appear in $z$, we should have $390$ in $V$

I am stuck with this. How to find out whether $910,546,390$ are not appearing in any of the columns in $w,x,y,z$??

entrelac
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Hari
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  • This is from Problem #25 in this contest. – r.e.s. Aug 19 '15 at 18:03
  • I'm not sure you asked the question you meant to. First you give conditions for $2731$ to appear in column X,Y,Z (column W might have been an oversight) based on contents of $V$, but then you ask "to find out whether 910,546,390" do not appear in $W,X,Y,Z$. This seems a non sequitur. – hardmath Aug 19 '15 at 18:20
  • @hardmath 910 appears in $V$ iff $3\times 910+1=2731$ appears in $X$. The problem is to find which columns $2731$ appears in - so these equivalences reduce the size of the problem. – Mark Bennet Aug 19 '15 at 18:25
  • @hardmath The contest was Feb 2015 – Mark Bennet Aug 19 '15 at 18:34

1 Answers1

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Here is a helping hand. Working with $Z$ we have $$2731\in W \iff 390 \in V$$

Now this will happen iff $390$ doesn't appear earlier in the table. $390 =389+1$ and $389$ is not divisible by $2,3,5,7$ so it can't appear earlier.

We also have $$2731\in X \iff 910\in V$$

Now $910=909+1$ and $909$ is divisible by $3$ but not $2,5,7$. If $303\in V$ then $910$ is excluded. So $$910\in V \iff 303\notin V$$

And work systematically back to reduce the numbers involved. For example, if $303$ is excluded, where will it appear in the table?

Mark Bennet
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