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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Comments
I like this teaser. Good job!
Thank you, really enjoyed this - came up with 28 first (thinking the square was not solid).
Also, isn't the second triangular number 3?
Sure is h!
That answer is wrong. 12 is the correct answer. You can have a triangle with 4 on each side and a square with 3 on each side. It's not so hard.
I agree that 12 is the answer but it is with a triangle with 5 on each side and a square with 4 on each side.
Oh, never mind last comment. Didn't catch the part about the shapes being SOLID. Sorry.
Nothing states that the square is also solid. Therefore, I came up with 28, which is also a triangle number.
I came up with 12... forgot about the shape being solid...
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