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by Brian Gladman on November 16, 2020

New Scientist Enigma 586 – The Paint Runs Down

by Keith Austin

From New Scientist #1739, 20th October 1990

In the diagram the lines indicate pipes for the paint to flow down. At each of A, B and C either red or blue paint is poured into the top of the pipe. The circles are paint processors. For the circles marked with a star, if all the paint flowing down into the circle is red then blue flows out of the bottom of the circle, otherwise red flows out. For the other circles, if all the paint flowing into the circle is blue, then blue flows out of the bottom otherwise red flows out. For example, if red is poured into the top of A and C and blue into B, then blue flows out of the pipe 5 and red out of pipes 1, 2, 3, 4, 6 and 7 at the bottom.

Some of the seven numbered bottom pipes are to be directed into a storage drum in such a way that the following condition holds whatever the choice of three paints put in A, B, C:

If red is poured into A then at least one pipe into the drum brings blue;
if blue is poured into A then all the pipes into the drum bring red.

Which of the numbered pipes should go into the drum?

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