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Problem of the Week
Problem B
A Pentagon Puzzle

To solve a puzzle, Jonah needs to insert a different number from \(1\) to \(10\) into each of the the ten circles in the diagram so that the three numbers on each side of the pentagon have the same sum. He calls this sum the magic sum.

A regular pentagon has a circle placed on each of its five corners. A circle is also placed at the midpoint of each of the five sides.

  1. What is the least possible sum of any three of the given digits? What is the greatest possible sum of any three of the given digits?

  2. Do you think either of the sums in part (a) could be the magic sum? Explain.

  3. Find a solution to the puzzle.

Extension: Can you find a different solution that is not a rotation or reflection of your solution from (c)?

Theme: Number Sense