Which Bike Is Free?

In this puzzle we ask you to figure out how these bicycles are locked to each other.

Bart, Chang, and Omar rode their bicycles to school. Each had a chain and a lock. Bart locked his bike to a lamppost and to Chang’s bike. Chang locked his bike to the lamppost and also to Omar’s bike. Omar locked his bike to the lamppost and to both Bart's and Chang’s bikes. Each bike was now held by two locks.

Bikes

Later that day Bart lost his key! With the two keys they had left, they could unlock only one of the bicycles. Whose bicycle was it?

Course:

Math [1]

Result/Solution(s)

Solution: Which Bike Is Free? Math Puzzle

To help figure out this puzzle, we drew a diagram. To keep it simple, we drew the bicycles as circles and the lamppost as a gray dot.

solution

We realized that we didn’t have to chain all the bikes as described in the puzzle and then remove two of the chains. The only important information is which bikes Bart’s chain had locked up. What Omar or Chang did is unnecessary information, since in the end they removed their chains. Since Bart chained his bike to the lamppost and to Chang’s bike, those two bikes remained tied up. Omar’s bike was free.

math [2]
Math Puzzle [3]