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Math brain teasers require computations to solve.

 Puzzle ID: #49969 Fun: (2.74) Difficulty: (2.23) Category: Math Submitted By: eighsse

5 free throws, 12 2-point shots, and 1 3-point shot.

Let x be the number of free throws made,
y be the number of 2-pointers made,
and z be the number of 3-pointers made.

From the score, you know (A): x + 2y + 3z = 32
From the quote, you know (B): x + y + z = 18
Multiply (B) by 3 to get (C): 3x + 3y + 3x = 54
Subtract (A) from (C) to get: 2x + y = 22, or (D): y = 22 - 2x
From the quote, you also know (E): 2x <= y
Substituting (D) into (E) gives: 2x <= 22 - 2x, or (F): x <= 5.5

If x=5, then from (D) you get y=12, and from (A) you get z=1.
If x=4, then y=14, and z=0.
If x=3, then y=16, and z=-1. This is not possible because z cannot be negative. If you continue decrementing x, then z will continue to decrease too.

So, you have two options that fit the criteria given by your brother:
5 free throws, 12 2-point shots, 1 3-point shot, or
4 free throws, 14 2-point shots, 0 3-point shots.
So it's a good thing that you heard that your favorite player made a 3-pointer, because that eliminates the second option!

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