Hint: Work backwards with each churn containing 18 gallons.
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.
Last week I decided to cycle to my Grandmother's house.
On the first day, I cycled half of the distance.
On day 2, I cycled one half of the remaining distance.
On day 3, I cycled three quarters of the remaining distance.
On day 4, I cycled 10 miles.
On day 5 I cycled two thirds of the remaining distance and on the final day I cycled the remaining 5 miles.
On the final day I cycled the remaining 5 miles
On Day 5 I started with 15 miles (as I cycled two thirds, leaving 5 miles).
On Day 4 I started with 25 miles (as I cycled 10 miles).
On Day 3 I started with 100 miles (as I cycled three quarters, leaving 25 miles).
On Day 2 I started with 200 miles (as I cycled half, leaving 100 miles).
On Day 1 I started with 400 miles (as I cycled half, leaving 200 miles).
How many squares, of any size, can you find on this chess board which do not contain a Rook?
There are 60 squares of size 1x1. There are 33 squares of size 2x2.
A total of 60 + 33 = 93.