Here the digital roots of the six numbers are 6, 4, 1, 2, 7, 9, which
together sum to 29, whose digital root is 2. As the contents of the
barrels sold must be a number divisible by 3, if one buyer purchased
twice as much as the other, we must find a barrel with root 2, 5, or 8
to set on one side. There is only one barrel, that containing 20
gallons, that fulfils these conditions. So the man must have kept these
20 gallons of beer for his own use and sold one man 33 gallons (the
18-gallon and 15-gallon barrels) and sold the other man 66 gallons (the
16, 19, and 31 gallon barrels).