1. A flask contains 40 liters of milk. How can you transfer 6 liters of milk from it into a 10-liter bucket using a 9-liter and a 5-liter bucket?
Solution. We fill the 5-liter bucket with milk and pour it into the bucket. Then we fill the 5-liter bucket again, pour it into the 9-liter bucket, fill the 5-liter bucket once more, and pour the missing 4 liters into the 9-liter bucket. Then, exactly 1 liter remains in the 5-liter bucket, which we pour into the bucket.