Tupper's inequality is $$\frac{1}{2}\lfloor mod(\lfloor \frac{y}{17}\rfloor 2^{-17\lfloor x\rfloor -mod(\lfloor y\rfloor ,17)},2)\rfloor .$$ Let's see if it holds for $x=0$ and $y=103$ Firstly, we have $$\lfloor \frac{y}{17}\rfloor =\lfloor \frac{103}{17}\rfloor =\lfloor 6.06\rfloor =6.$$ Secondly, we have $$17\lfloor x\rfloor =17\lfloor 0\rfloor =0.$$ We also have $$mod(\lfloor y\rfloor ,17)=mod(\lfloor 103\rfloor ,17)=mod(103,17)=1.$$ Putting all this together gives $$\lfloor mod(\lfloor \frac{y}{17}\rfloor 2^{-17\lfloor x\rfloor -mod(\lfloor y\rfloor ,17)},2)\rfloor =\lfloor mod(6\times 2^{0-1},2)\rfloor =\lfloor mod(\frac{6}{2},2)\rfloor =\lfloor mod(3,2)\rfloor =1.$$ Since $\frac{1}{2}1$ the inequality holds for $x=0$ and $y=103$. Therefore, the square with coordinates $(0,103)$ should be coloured. Can you work out whether the square below, which has coordinates $(0,102)$, should be coloured?

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