Competition problem — Number theory

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Number theory Difficulty 2.4 Junior Find the answer Netherlands

A baker baked a big square cake. He wants to cut the cake. He cuts the cake only lengthwise or widthwise, all the way from one edge to the opposite edge.
At least how many cuts does the baker need in order to cut the cake into exactly $180$ pieces?
A) $25$ B) $26$ C) $27$ D) $28$ E) $29$

This was a multiple-choice question, but the options didn't survive into the source we have. The answer given is A, and the solution below works it through.

Solution

A) $25$

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Source: MathNet, licensed CC-BY-4.0. Statement and solution reproduced as published; topic and difficulty added by this site.