A witch needs to brew a potion with exactly 4 cups of liquid. She has an 8-cup cauldron and a 3-cup cauldron, but no markings. How can she measure exactly 4 cups?
Hints
Pour between containers and keep track of what remains.
Answer
Fill the 8-cup cauldron. Pour into the 3-cup until full (leaving 5 cups). Empty the 3-cup. Pour the 5 cups into the 3-cup (leaving 2 cups). Empty 3-cup again. Pour the 2 cups into the 3-cup. Fill 8-cup again. Pour from 8-cup into 3-cup until full (adding 1 cup), leaving exactly 7 cups. Actually, easier: Fill 8-cup, pour 3 cups out, leaving 5. Pour 3 more out, leaving 2. Fill 8-cup again, pour 2 cups to fill the 3-cup container (which had 1), leaving 6. Pour out 3, leaving 3. Pour out remaining 3 from other container. Transfer the 3. Fill 8, pour 1 to top off the 3-cup, leaves 7. Empty 3. Pour 3 from 8 (leaves 4). Or simpler: Fill 3, pour into 8. Fill 3 again, pour into 8 (now has 6). Fill 3 again, pour into 8 until 8 is full (needs 2 cups), leaving 1 cup in 3-cup. Empty 8. Pour the 1 cup into 8. Fill 3, pour into 8 (now has 4 cups).