Olympiad Maths Prep

Track / Stage 4 / 148 of 340 #408 of 2000

Problem 408

AMC 12 late, AIME early
Combinatorics Difficulty 4.8 Find the answer

3. Cut the figure shown in the diagram into two parts that are identical in size and shape. You can cut along the grid lines and along the diagonals of the squares. Two parts are considered identical if, after cutting, they can be placed on top of each other so that they fit exactly. They can be rotated and flipped.

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This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

Solution. One of the options is shown in the figure below.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.