A fair dice is tossed 6 times. What is the probability that there is at least one pair of identical consecutive face values?

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For example, 231146 is a valid sample point but 131213 is not. This is a question on past exam that i have no idea to solve. Please help me!

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Hint: How many throws are there for the first one that don't spoil the string? How many throws for the second? The third?