Rearrange Paper

There is a square piece of paper with a hole that is denoted by the circle on the top right side in the given picture. You have to cut the paper in a manner that it forms two and only two separate pieces of paper and then rearrange the pieces in a manner that the holes come in the centre of the paper.

Rearrange Paper




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When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
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When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
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When I looked for a smaller number with this property I couldn't find one.

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The following question it puts forth you:

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There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.