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TSA 2013 · Question 37 · Optimisation

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I have a bird automaton that, when activated, flaps its wings and whistles three different tunes successively, selected at random from its repertoire of ten. It performs one of its ten tunes for 10 seconds, six of them for 15 seconds each and three of them for 20 seconds each.

When my granddaughter visits she is fascinated, activating it again and again as soon as it stops each time. On her last visit she kept it going for a whole hour, and I lost count of how many times she activated it.

What is the maximum number of times that my automaton could possibly have been activated during one hour?