A and B have an 8 gallon cask full of wine, which they wish to divide into two equal parts, and the only measures they have are a 5-gallon cask and a 3-gallon cask. How shall they make the division with these two vessels?
One possible method (others possible). First fill the 3-gallon cask from the 8-gallon cask; then pour these 3 gallons into the 5-gallon cask; then fill the 3-gallon cask again, and fill the 5-gallon cask from the 3-gallon cask; this will leave 1 gallon in the 3-gallon cask; then empty the 5-gallon cask into the 8-gallon cask, pour the 1 gallon from the 3-gallon cask into the 5-gallon cask, and fill the 3-gallon cask from the 8-gallon cask. There will then be 4 gallons in the 8-gallon cask.