Maths Olympiad Prep

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Problem 1036

AMC 12 late, AIME early
Combinatorics Difficulty 5.0 Find the answer Dutch Mathematical Olympiad · Netherlands

There is a power plant in the cell indicated by CC. The cells indicated by XX are places to which the power plant should be connected. This requires electricity masts in some cells, which we can indicate by placing an MM in that cell. Two cells with a letter in them can be connected by a cable if the cells are adjacent at a side or a vertex. Ultimately, each cell with an XX must be connected to the power plant via one or more cells with the letters MM or XX.

XXXX
XXXX
XXCC
XX

What is the minimum number of electricity masts needed?
A) 3 B) 4 C) 5 D) 8 E) 9

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.

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Official solution

B) 4

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