Black and white tiles

Algebra Level 2

Hagar has $2018$ black square tiles and $2020$ white square tiles. All tiles are of the same size. Hagar was asked to build the largest possible square similar to the one given in the figure. How many white tiles are left after completing the largest possible square?

The answer is 35.

1 solution

Jerry McKenzie
Jan 18, 2018

Easily we can see $\lfloor \sqrt{2018+2020} \rfloor ^2 = 63$

So 63 is the largest side of such square. Since 63 is odd we will use 1 more black tile than white tile, if we allow black to have the corners.

$\frac{63^2-1}{2}=1984$

So 1984 is how many white tiles are used and 1985 black tiles. This means 2020-1985=35, and 35 black tiles are left over.

Black and white tiles

The answer is 35.

1 solution

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