February 2021
Problem of the Month

NBA Playoff

During last year's NBA Playoffs, an announcer complained that a player had just fouled James Hardin on a 3-point shot.   The announcer pointed out that Hardin hits 87% of his free throws and 37% of his 3-point shots.   He went on to say that you should just let him shoot the 3-point shot and NOT foul because you are just giving him an additional one and a half points on each attempted 3-pointer.

Determine the actual number of points that a player is giving James Hardin on each attempted 3-pointer if he is fouled.
Show your computations.

NOTE: If a player makes a three point shot, his team is awarded 3 points.
If a player is fouled on a 3-pointer and he misses the shot, then he is awarded three free throws (and each free throw counts one point if he makes it).

Solution to the Problem:

The answer is 1.5 points per attempt, so the announcer was exactly right.

Compare the number of points Hardin would make in 100 attempts if he is fouled and if he is not fouled.

100 3-pointers and NOT fouled:
37 x 3 = 111 points.
100 3-pointers and IS fouled:
87 x 3 = 261 points.

So he makes 150 more points
on 100 3-point attempts.

That is exactly 1.5 points more per attempt.

Correctly solved by:

1. Ivy Joseph	Pune, Maharashtra, India
2. Colin (Yowie) Bowey	Beechworth, Victoria, Australia

Send any comments or questions to: David Pleacher