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# Who finished 2nd?

## Question

Al, Bert, and Charlie competed in a track and field event in which points were awarded for 1st, 2nd, and 3rd, 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 1st in the shot put. Who finished 2nd in the javelin throw?

This is a Gold star puzzle.

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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 by bonanova
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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 by bonanova
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Clarification questions:

Are points awarded in integers?

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

Edited by Molly Mae

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Yes and yes.

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