We are counting in whole numbers always starting at the number 1.
1,2,3,4, …
Schur numbers tell you the highest number that you can count to using k different colours before you’re forced to have an all same-coloured solution to a + b = c.
Example
Is this a valid colouring for k = 3 (3 colours)?
No, because 2 + 2 = 4, 1 + 5 = 6 and 1 + 6 = 7 and same coloured sums are not allowed.
Challenge
For 1 colour, let’s say red, we can only count up to the number 1 like this:
1
For 2 colours, let’s say red and blue, we can count up to 4 like this:
1 2 3 4
Can you explain why we can’t add the number 5?
What is the highest number you can count to using 3 colours?
You can check solutions here:
See here for the printable puzzle with further explanations and here for a video including the solutions (that are known so far …).