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Math and Logic

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Who Won the Race?

How much information do you need to find the finish order of a three-person race? It turns out, not much at all.

Suppose that in the race above among Annie, Becca, and Carlos, we only know that Becca finished before Carlos. What are the possible orders for the entire race?

There are actually only three possible orders in which the runners could have finished, and we can see that by considering the unknown in this problem: where did Annie finish?

Since the relationship between Becca and Carlos is known, we only need to know Annie's place in the race to determine where everyone finished. However, it is possible to learn another piece of information that doesn't lock things down completely. Here's an example:

Annie finished after Becca.

While we now know that Becca was first, there are still two places where Annie could be—in front of or behind Carlos.

In the problem below, you'll be putting together information like this, but with four runners instead of three. Take your time and use logic to figure out the order.

Today's Challenge

Four runners compete in a race: Annie, Becca, Carlos, and Dante.

After some confusion at the finish line, it's unclear what the final finishing order was, but the following information is known:

  1. Dante finished before Annie.
  2. Becca wasn't third.
  3. There were two runners between Annie and Carlos.

Who won the race?

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