# Digit-colouring puzzle



## robert@fm (Sep 15, 2018)

Write the digits 1 to 9, and colour them either red or blue (use any choose method you like), thus:

1 2 3 4 5 6 7 8 9

In the above, there are four monochromatic arithmetic progressions (APs) of three digits (all red, as it happens); as well as the obvious 4 5 6, there are also 2 4 6, 4 6 8 and 2 5 8.

Is it possible to do the colouring in such a way as to have _no_ AP of three digits, all the same colour? Prove your answer...


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## robert@fm (Sep 3, 2020)

Bumping this as nobody has answered.


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## chaoticcar (Sep 3, 2020)

It's cos we don't know 
  Carol


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## Docb (Sep 3, 2020)

123456789? Nope, 147 in blue.

Brain too addled these days to try and work out a general solution. Up to 8 numbers easy to do by trial and error but adding the 9 in throws a wobbler.  I suspect it is not possible so I will think about it for a bit more.  I'm an old enough puzzler to want to delay as long as possible before looking it up on tinternet.


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