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Problem 366

Geometry Difficulty 2.5 Find the answer CEMC Fermat

How many interior intersection points are there on a 12 by 12 grid of squares?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

A 12 by 12 grid of squares will have 11 interior vertical lines and 11 interior horizontal lines. Each of the 11 interior vertical lines intersects each of the 11 interior horizontal lines and creates an interior intersection point. Therefore, the number of interior intersection points is 11imes11=12111 imes 11=121.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.