1248136Number 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 \(813.\)