Open the Tap
Read the puzzle
Pipe joints sit on a grid: columns 1 to 5 from the left, rows 1 to 4 from the top; (3,1) means column 3, row 1. The tank feeds (3,1). Plain pipes: (1,1)-(2,1); (1,1)-(1,2); (1,3)-(1,4); (2,1)-(2,2)-(3,2)-(3,3); (2,3)-(2,4); (3,3)-(3,4); (4,1)-(4,3); (4,1)-(5,1)-(5,2), a dead end; (4,3)-(5,3). Open valves: (2,1)-(3,1); (2,3)-(3,3); (3,4)-(4,4); (5,3)-(5,4). Closed valves: (3,1)-(4,1); (3,3)-(4,3); (1,4)-(2,4); (4,4)-(5,4); (1,2)-(1,3). Jars hang below (1,4) for A, (2,4) for B through a closed valve, (4,4) for C and (5,4) for D. Which jar fills?
Valves stay as shown. Which jar fills with water?
JAR C
Every other route ends at a closed valve.
How to solve it
Start at the tank and spread the water through every pipe it can reach, stopping at any valve whose handle lies across the pipe.
From the tank the water cannot go right, because the first valve on that side is closed. Going left, the valve is open, so water reaches the top-left corner and runs down the left edge, but the valve partway down is closed, so jar A gets nothing that way. The water also drops down the second column, steps right along a short pipe and runs down the middle column to the junction in row 3.
At that junction the right-hand valve is closed and the left-hand valve is open. Going left and down the second column leads only to two closed valves, one toward A and one just above jar B. Going straight down the middle column reaches row 4, where an open valve lets water across to the fourth column and down into jar C. The valve beyond it, toward D, is closed, and the other ways to D start behind the closed valves already met at the top and at the row 3 junction, so D stays dry.
Only C has an open route. The usual mistake is reading a handle that crosses a vertical pipe as open; across the pipe always means closed.
