Say, the Players Department has locked 100 accounts in the past. But to keep a stable number of players, a decision was made to every once in a while grant amnesty to locked out ex-players.
However, the PD was without a Chairman for a while, and the new Chairman had a weird sense of humor. He asked one of his fellow staff members to come up with a fun way of unlocking people. It should involve multiple locking and unlocking of accounts, and in the end, not too many acounts should be unlocked.
To his surprise, one of his fellows immediately had a proposal to make.
'Let's do that in 100 steps', he said. 'First, we unlock every account. Then, we lock every second account again. Then, for every third account, we lock the ones that were unlocked, and unlock the ones that were locked. Then we do the same for every fourth account. And so on, until we flip the status of every 100th account during the 100th step.'
They all liked the playful character of that idea, but they didn't know how many of the originally locked accounts would remain unlocked after that procedure.
Can anyone help them?
[edit: Slightly altered the algorithm. If anyone had an idea for a correct answer, they will easily adapt to the new algorithm.]
