# Square covered with tiles

A square $666\times666$ has been covered using tiles $5\times1$. A single square $1\times 1$ hasn't been covered. Find in how many places the not covered square can be.

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How can a single square be in more than one place? –  Marc van Leeuwen Sep 20 '12 at 11:47
There's a similar problem here, involving an $8\times 8$ square covered with $3\times 1$ tiles. –  MJD Sep 20 '12 at 12:12

## 1 Answer

Hint: Can you colour the individual squares with $5$ different colours such that any $5\times1$ tile covers one square of each colour? If so, what can you say about the colour of the uncovered square? Can you do this colouring in two similar but different ways? If so, the uncovered square must have the right colour in both colourings. Can you exhibit for each of the squares with the right colours an explicit covering that leaves that square uncovered?

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OK I UNDERSTAND. Can you vote up my question so that i have the reputation to vote up your answer? –  pagla Sep 20 '12 at 10:55
@pagal You can also accept an answer by clicking on the shadowed check mark next to the answer. –  amWhy Sep 20 '12 at 11:11