# Hints (preferably the underlying theory)

Does anyone have any (preferably theory based) hints on how to derive a solution?

I’m having trouble working out how to get every third blue to set off a red, when bits are binary and the output repeats…

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Worked it out

For anyone else having trouble… If you count one twice, when you count two it’s actually three

(Thought I’d better make it a little cryptic)

Can you set up the system to count to 2? Place an interrupt that will catch the third ball. Then, replace the interrupt with ramps that will trigger the opposite color. Next you could go back to challenge 4 where the red ball triggers the blue. A crossover will go in there somewhere as in challenge 5. I am not trying to insult your intelligence, but I’m simple-minded myself and I work with elementary-age children.

What I try to do with my students is to have them break problems down into solvable parts, and then try to make those parts fit into the big picture. I guess the “theory” would be out of Polya’s “How to Solve It”. Being a detective, in other words, creating the algorithm is the fun part. Applying it to derive a solution is just a matter of plugging in the numbers.

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