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Math and Logic

Misleading Marathoners

Toggle Tags puzzles provide a list of constraints that the characters in the puzzle need to satisfy.

Read on for some examples, or jump straight to the puzzle below.

With these puzzles, the goal is to use the buttons to indicate what each character in the puzzle has or did so that all of the constraints are satisfied. By clicking the right arrow below the puzzle, you can view a demonstration of a puzzle solution complete with the underlying logic. If you need to see a step again, click the left arrow.

Five friends — Ivy, Jayden, Kurt, Laura, Maria — have gone out to a game together, and they're each wearing either a purple or yellow baseball cap.

As before, you can use the arrows below the puzzle to see the steps of a solution with logic. This puzzle is a little more complicated than the first one, with some characters who might not tell the truth. Let's assume that all Londoners are either werewolves who always lie or humans who always tell the truth.

To solve a Toggle Tags puzzle, you can make a hypothesis and follow where it takes you — to a solution or a contradiction. Alternatively, you might be able to analyze one or more clues to find a more efficient starting point. See what strategy works for you in the challenge below.

Today's Challenge

Four runners participate in a race.

How many places apart did runners A and C finish?

Clarification: To compute how many places apart two runners are, subtract their places. For example, the 1st and 4th place runners are 41=3{4-1=3} places apart.

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