Examples of Problems

1. (Medium) A 10-litre tank is filled with kerosene. In addition to this tank, you have at your disposal a 7 liter container and a 3 liter container, both empty. How can you measure 5 liters of kerosene from the tank? Please note that there are no written measurements on the tank and containers.

2. (Easy) A clock with hands is 4 minutes slow. Three and a half hours ago, the clock was set exactly right. Now the clock shows 12 hours tapping. How long before the clock will show 12 hours of tapping again?

3. (Very easy) William and Lea were supposed to meet at 8:00 a.m. William thinks his watch is 25 minutes late, when in fact it is only 10 minutes late. Lea thinks her watch is 10 minutes late, when in fact it is 5 minutes early. What time will William and Lea be at the meeting point if they both want to arrive 5 minutes early?

4. Of 8 coins, one is counterfeit and is lighter. Determine the counterfeit coin by weighing it twice on a two-pan scale (without using any other weights).

5. Of 12 coins, one is counterfeit and has a different weight from the other coins. Using three weighings on a two-pan scale, determine the counterfeit coin and determine if it is lighter or heavier than the real coins.

The MSRI Mathematical Circles Library has compiled a list of books with many more problems that can be used in math circles.