Maths problem 00/03/2009

[Wongo]

My mate Groggy gave me this challenge the other day. I found it interesting. Do you want to have a go?

In my daughter's school, there are 100 lockers, numbered 1 to 100; the summer break also happens to be exactly 100 days long; and even the cleaners are interested in numbers.

On the first day of summer, all the lockers are unlocked. The cleaner then walks by and, for every locker, locks it if it was unlocked, and unlocks it if it was locked. (Since all the lockers were unlocked, that means he locks each one.)

On the second day, the cleaner walks by and, for every 2nd locker starting with #2, locks it if it was unlocked, and unlocks it if it was locked. (Since all the lockers were locked after the first day, that means he unlocks each one.)

On the third day, he walks by and, for every 3rd locker starting with #3, locks it if it was unlocked, and unlocks it if it was locked. (Now, some lockers get locked and some unlocked.)

On the Nth day, of course, he walks by and, for every Nth locker starting with #N, locks it if it was unlocked, and unlocks it if it was locked.

After 100 days, how many lockers are locked?

[Groggy]

I'll be interested to see if anyone can beat Wongo's time

[Wongo]

BTW groggy, there is very little to do with binary. Your hint didn't really help.

[Groggy]

If you were a lateral rather than a logical thinker, it would have been obvious

[Wongo]

I don't agree with you.

[fenderbelly]

none ---they open them all for the kids returning to school

[switt775]

For 100 lockers, the answer is 10.

Hint: The answer is 10 for any number of lockers between 100 and 120.

[Wongo]

10 is the right answer.

What is the hint for?

[journeyman Mick]

Why is the bloody cleaner mucking around locking and unlocking lockers instead of cleaning? I think that's a question of much greater importance.

Mick

[mic-d]

Why is the bloody cleaner mucking around locking and unlocking lockers instead of cleaning? I think that's a question of much greater importance.

Mick

and not even God had to work 'til the Nth day

Cheers
Michael

[switt775]

10 is the right answer.

What is the hint for?

Are you asking me to reveal the calculation method, or do we leave it hanging a little longer?

[Wongo]

Mick

[Wongo]

Are you asking me to reveal the calculation method, or do we leave it hanging a little longer?

Does your hint really lead people to the right answer? I do not think so. Probably just as bad as groggy's.

[switt775]

Does your hint really lead people to the right answer? I do not think so. Probably just as bad as groggy's.

So as not to spoil the fun for everyone, I'll PM you the answer.

[Wongo]

Hey switty, you should come to the drivel forum on Fridays. Groggy gives me one of these every time. I am sure you will enjoy it as much as I do. It is fun.