Art of Problem Solving

2025 AIME II Problems/Problem 3: Difference between revisions

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==Problem==
==Problem==
Four unit squares form a <math>2 \times 2</math> grid. Each of the <math>12</math> unit line segments forming the sides of the squares is colored either red or blue in such a say that each unit square has <math>2</math> red sides and <math>2</math> blue sides. One example is shown below (red is solid, blue is dashed). Find the number of such colorings.
Four unit squares form a <math>2 \times 2</math> grid. Each of the <math>12</math> unit line segments forming the sides of the squares is colored either red or blue in such a say that each unit square has <math>2</math> red sides and <math>2</math> blue sides. One example is shown below (red is solid, blue is dashed). Find the number of such colorings.
== Solution ==

Revision as of 22:00, 13 February 2025

Problem

Four unit squares form a $2 \times 2$ grid. Each of the $12$ unit line segments forming the sides of the squares is colored either red or blue in such a say that each unit square has $2$ red sides and $2$ blue sides. One example is shown below (red is solid, blue is dashed). Find the number of such colorings.

Solution