Who finished 2nd?

[bonanova]

Al, Bert, and Charlie competed in a track and field event in which points were awarded for 1^st, 2^nd, and 3^rd, place only. At the end of the day, Al had accumulated 22 points, while Bert and Charlie each garnered only 9 points. No other competitor earned points. Bert was 1^st in the shot put. Who finished 2^nd in the javelin throw?

This is a Gold star puzzle.

[Molly Mae]

Clarification questions:

Are points awarded in integers?

I'll also assume that the points are 1st>2nd>3rd>0, since this is obvious.

Edited April 5, 2018 by Molly Mae

[bonanova]

Yes and yes.

[plainglazed]

answer

Spoiler

Charlie.  Thought I was close this morning in the shower but it wasn't until my commute into work that I realized that possibility was indeed unique.  Will leave the details to MM .Very fun puzzle my friend.

Edited April 7, 2018 by bonanova
Gold Star

[Molly Mae]

EDIT:Ninja'd by PG.

A little bit of trial and error based on some observations:

 

The total points scored is 40, so if we assume integer points per place, we know that each event gives a total number of points that's a factor of 40 AND that the total number of events is also a factor of 40 AND that those two numbers multiplied by each other equals 40.  A little jumping around and I came up with these values:

1st Place is worth 5 points, 2nd is worth 2 points, and 3rd is worth 1 point.  Total points given per event = 8, so there must be 5 events.

We know Bert has 5 points for one event, so he must have 4 third places

Bert: 1 / 0 / 4

Al is easy to calculate.  There's only one configuration that works to get to 22 points in 5 events:

Al: 4 / 1 / 0

So we can fill in the rest based on places that weren't taken:

Charlie: 0 / 4 / 1

These equal the correct point totals.

Since Bert got 1st in the shot-put, we know that his 1st place didn't come from the javelin.  So Al must have taken 1st in the javelin.  Bert didn't get a second place at all, so Charlie must have gotten 2nd in the javelin.

Edited April 7, 2018 by bonanova
Gold Star for method