### Brain Teasers

# Halftime Formations

The vicinity high school marching band is planning a halftime show for the big football game of the season. As part of the show, they want to march onto the field in the formation of a triangle (forming a solid equilateral triangle) and then rearrange themselves into a square (forming a solid square).

What is the minimum number of marching band members needed to do this?

Note: the marching band has more than 1 person in it

What is the minimum number of marching band members needed to do this?

Note: the marching band has more than 1 person in it

### Answer

The marching band needs 36 members in order to perform this maneuver.Triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36 etc... Square numbers are 1, 4, 9, 16, 25, 36 etc... Other than 1 the next possible number to appear in both lists is 36.

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