Question 185
Let $n \geqslant 1$. We have finitely many bottles, each containing an amount of water less than 1 liter, such that the total amount of water is $\frac{n}{2}$ liters. We also have $n$ empty buckets.
Show that it is possible to empty each bottle into a bucket (several bottles may be emptied into the same bucket, but a bottle may not be partly emptied into one bucket and partly into another) so that each bucket contains at most 1 liter of water.
Show that it is possible to empty each bottle into a bucket (several bottles may be emptied into the same bucket, but a bottle may not be partly emptied into one bucket and partly into another) so that each bucket contains at most 1 liter of water.