# Application of Bézout's identity to sand timer puzzles

This article has been titled for teachers. When you bring up this topic, you should do so under a heading that excludes mention of Bézout's identity, as it's a give-away on how to solve these types of puzzles.

You have two sand timers, one measures 9 minutes, the other, 13 minutes. Can you measure 30 minutes?

You have two sand timers, one measures 7 minutes, the other, 11 minutes. Can you measure 15 minutes?

You have two sand timers, one measure $$a$$ minutes, the other, $$b$$ minutes. Which durations can you measure?

Can you measure other durations if you're allowed to pause the timers (set them on their sides)?

Once your students have struggled with these questions for a while, give them this to read.

Sources:

• The Inquisitive Problem Solver (problem 7)
• Cut the Knot