You have two hourglasses: 7-minute and 11-minute. How do you measure 15 minutes?

You have two hourglasses: 7-minute and 11-minute. How do you measure 15 minutes?

Approach: Start both, flip at appropriate times.

Start both. When 7 runs out, flip it (4 min left on 11). When 11 runs out, flip 7 (3 min left on 7). When 7 runs out, 15 minutes have passed.

Follow-up: What times can be measured?

Key concepts: linear combination, timing, synchronization.