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Scott repeatedly rolls a pair of standard six-sided dice and keeps track of the sum of the two numbers rolled each time. So far he has not rolled any sum twice. What is the maximum possible number of times he has thrown the dice?

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So there are

11 different outcomes for 6-sided pairs of dice, from 2 to 12. He could therefore have rolled the dice a maximum of 11 different times to get each of the different outcomes exactly once.

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