# Alan's 3N Game

**Number Theory**Level 4

Alan and Bob are playing with numbers. Starting with the number \(N=1\) they take turns performing arithmetic manipulations with \(N\). Alan goes first and always multiplies the current number by \(3\). Bob adds \(1\) or \(2\) to the current number, depending on a coin toss. A number is called reachable, if it can possibly appear in this game. How many reachable numbers are there between \(1\) and \(1000\) (inclusive)?

**Details and assumptions**

Number \(1\) is considered reachable.

Alan's first step would be to multiply 3 to 1, getting 3, which becomes the current number. Bob then adds either 1 or 2 to the current number (which is 3), depending on the coin toss.