The Indecisive Gamekeeper
duke loved to invite his friends to hunt pheasant on his estate.
His gamekeeper was responsible for stocking the woods with plump
birds. He kept one hundred pheasants each locked in its own
cage to protect against poachers. The cages were numbered from
1 to 100. Each cage had a lock that opened when the key was
turned once, and locked again when when it was turned a second
The gamekeeper began feeling sorry for his charges.
One night, while the birds slept, he quietly unlocked all 100
cages. At once he began worrying that the duke would be furious
and immediately went back and turned the locks again on every
second lock (2, 4, 6, ...), thereby locking them.
Thinking that he had still freed too many birds,
he gave every third lock a turn (3, 6, 9, ...), then every fourth
lock, then every fifth lock, sixth lock, and so on, all the
way to the "every 100th" lock. He finished just in
time, as dawn was breaking, and the birds were beginning to
Your task is to find:
- Which cages will be left open? Can you figure out why?
- How many locks, and which ones, will be turned exactly
Extra: Which cages(s) was (were) switched the