**Answer:**
12, 33 and 9 gallons respectively for churns 1, 2 and 3.

The solution may require more than one read!

Before After Therefore

>> Pour 1 C1 = 12 C1 = 9 C2 = +3

>> Pour 1 C2 = 33 C2 = 36

>> Pour 2 C2 = 36 C2 = 18 C3 = +18

>> Pour 3 C3 = 27 C3 = 18 C1 = +9

>> Pour 3 C1 = 9 C1 = 18

To explain a little further. After pour 3, C3 must have contained 18 gallons, so it must have contained 27 before the pour. Similarly after pour 2, C2 must have contained 18 gallons, so must have contained 36 before the pour. After pour 3, C1 must have contained 18 gallons, and it received 9 gallons from pour 3, so must have had 9 before the pour. So pour 1 left 9 gallons in C1, which means C1 contained 12 before the pour and C2 received 3 gallons. We know that C2 had 36 gallons before pour 2, so must have started with 33 gallons. QED!