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Problem 307

Number theory Difficulty 2.4 Find the answer Junior Mathematical Olympiad · 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, so there is nothing here to pick from. Work it on paper and mark yourself against the solution below.

Official solution

A) $25$

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.