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+--- Thread: Logic Challenge (/showthread.php?tid=32594)
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Logic Challenge - Shidoshi - 2010-11-11
Assume you have 1 million doors, they are all closed.
You will do 1 million operations of opening/closing doors.
At operation number 1 you close (the ones opened) and open (the ones closed) that are multiple of 1
At operation number 2 you close (the ones opened) and open (the ones closed) that are multiple of 2
At operation number n you close (the ones opened) and open (the ones closed) that are multiple of n
.
.
.
At operation number 1,000,000 you close (the ones opened) and open (the ones closed) that are multiple of 1,000,000
How many open doors do you have at the end?
Logic Challenge - Mute - 2010-11-11
1,000,000.
Logic Challenge - butterfλi - 2010-11-11
edit
Logic Challenge - Nikkey - 2010-11-11
1,000
Logic Challenge - Salguod - 2010-11-11
1
Edit: Misread; I should've known that would be too easy.
Logic Challenge - Jedward - 2010-11-11
0
Logic Challenge - KaidaTan - 2010-11-11
Ugh, I'm not good at this type of thing. The only thing I'm sure of is that all the prime-numbered doors would be closed. But that's easy.
Okay... so basically if something has an even number of factors, it's closed. If it has an odd number of factors, it's open. Not sure how you could devise a way to do figure that out without having to systematically go through each door and figure out if it's open or closed; which is something I think the million is trying to discourage.
Logic Challenge - Kalovale - 2010-11-11
Uh, this seems impossible without chopping everything up with a chain of automated reiterations.
The first turn will turn everything (including the first door) open. Subsequent operations no long touch doors they already passed, thus certain (e.g the first door) or more precise every door up to 999th retains its state past a certain point.
The open/close states depend on the door's total number of factors, which so far I haven't seen the pattern for. Even the primes pose enough of a problem for me personally.
Logic Challenge - Shidoshi - 2010-11-11
Yeah, the 1,000,000 is supposed to discourage force-solving.
If you really want discouragement, use 10^90 doors.
Logic Challenge - Kalovale - 2010-11-11
69.
Logic Challenge - Kaasoljoyyx - 2010-11-11
Easy, all perfect squares of the form f(x) = x^2 are left open where x is an integer greater than 0.
Take the square root of the number, in this case it's 1*10^6, which simpliy equates to 1,000. In the case of a decimal, round down.
So what Jean/mondays said.
Logic Challenge - Kalovale - 2010-11-11
I see, whatever number of factors x has, the number of factors of f(x) is made even with the square. But how do you see the reverse, if X had an even number of factors, it is a perfect square?
Logic Challenge - WayOfTime - 2010-11-11
Even prime numbers would be closed, since they can be a factor of 1 and that prime number.
So the only doors that are open are: f(x)=x^2 where x is an element of the natural number.
Logic Challenge - Solarboy - 2010-11-11
You still have all doors, they never went anywhere, you jsut opened and closed them.
Logic Challenge - Shidoshi - 2010-11-11
Kaasoljoyyx Wrote:Easy, all perfect squares of the form f(x) = x^2 are left open where x is an integer greater than 0.
Take the square root of the number, in this case it's 1*10^6, which simpliy equates to 1,000. In the case of a decimal, round down.
So what Jean/mondays said.
=3
Logic Challenge - Takebacker - 2010-11-11
Solarboy Wrote:You still have all doors, they never went anywhere, you jsut opened and closed them.
He won.
Logic Challenge - ¬Rob - 2010-11-11
Solarboy Wrote:You still have all doors, they never went anywhere, you jsut opened and closed them.
Shidoshi Wrote:How many open doors do you have at the end?
Meep.
Logic Challenge - Solarboy - 2010-11-11
¬Rob Wrote:Meep.
Damn, read that wrong then.
Logic Challenge - Mute - 2010-11-11
Solarboy Wrote:You still have all doors, they never went anywhere, you jsut opened and closed them.
Takebacker Wrote:He won.
...
Mute Wrote:1,000,000.
i was right fir--
¬Rob Wrote:Meep.
DAMN YOU.
Logic Challenge - Daku - 2010-11-11
5. I got lazy.