# 1248136

Number Theory Level 5

Andy's little brother is playing a game with the list of powers of $$2:$$ $1,2,4,8,16,32, \ldots$ He chooses randomly one of the powers and then writes down a three-digit number made out of its first digit, then the first digit of the next number, then the first digit of the next number. How many possible different three-digit numbers can he write down?

Details and assumptions

As an explicit example, if Andy's brother chooses number $$8$$, then he writes down the first digits of 8, 16 and 32, which gives $$813.$$

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