Today’s example, known broadly as a distance puzzle, is a type that shows up often at competitions. It again showed up in one of today’s individual rounds.

The instructions: Fill in the circles with different integers, starting with 1, such that each pair of consecutive integers is farther apart than the previous pair. (Hint: You’ll have to do a little time-traveling back to high school geometry and dust off that Pythagorean Theorem!)

Here is an example of a solved puzzle: