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Omni-MATH / The workers laid a floor of size n×n (10<n<20) with two types of tiles: 2×2 and 5×1. It turned out that they were able to completely lay the floor so that the same number of tiles …

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problem

The workers laid a floor of size n×nn\times n (10<n<2010 <n <20) with two types of tiles: 2×22 \times 2 and 5×15\times 1. It turned out that they were able to completely lay the floor so that the same number of tiles of each type was used. For which nn could this happen? (You can’t cut tiles and also put them on top of each other.)
Plain-text mathematical notation (without MathML)
The workers laid a floor of size n×n (10<n<20) with two types of tiles: 2×2 and 5×1. It turned out that they were able to completely lay the floor so that the same number of tiles of each type was used. For which n could this happen?  (You can’t cut tiles and also put them on top of each other.)
Original LaTeX notation
The workers laid a floor of size $n\times n$ ($10 <n <20$) with two types of tiles: $2 \times 2$ and $5\times 1$. It turned out that they were able to completely lay the floor so that the same number of tiles of each type was used. For which $n$ could this happen?  (You can’t cut tiles and also put them on top of each other.)

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Source and history

task_id
91fc26dc-bb50-5362-b660-ba07f870c5f0
task_key
test--91fc26dc-bb50-5362-b660-ba07f870c5f0
task_revision_id
1
config / split
/ test

Official source

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