Logical puzzles with prizes!

[+Colibri]

I've decided to post a few logical problems here, there will also be prizes given to the person who finds the answer.


Lady and her pool
This one is worth 10ED. It's an easy one to get started.

A lady had a pool, surrounded by 4 trees.

She decided she wants to make the pool bigger, but doesn't want to loose her trees. What will she say to the engineer when he comes to plot out the new pool area?

[Daruma]

I don't quite understand the question...

What will she say to the engineer when he comes to plot out the new pool area?

She will say that she dosen't want to lose the pool?

Or has she already come up with a plan how to make the pool bigger and not chop dpown the trees?

Then you can just make it bigger, but make it like a + shaped pool

[+Colibri]

O right, lol i forgot one most important thing:
The pool must remain of a square shape.

So, she already knows how the pool needs to be enlarged, so that it will be inside the trees, bigger, and a square. Do you?

[Daruma]

can you move the trees?

[+Colibri]

Nope the trees have very deep roots. It's also not possible to make a pool with an island on it. So a simple square shaped pool with no extras in it. And surrounded by those same four trees.

[kriptologist]

Simple, make the pool deeper

[+Colibri]

Hehe, good idea... well she prefers this depth, so we're looking to just make the surface bigger.

[kriptologist]

Best I can figure is to move all four corners out until they run into the trees but not take them out. However if the trees are already right against the pool corners then that is not feasible. Gee.... an I pride my logic but ya got me stumped.

[kharn]

turn the pool round by 45 degrees then itll expand out a fair bit

[Rote]

turn the pool round by 45 degrees then itll expand out a fair bit

Very very good... Congrats.

[Alegur]

My first thought is to concur with Kharn, turning the pool 45 degrees gives a great deal of leeway. However, if the goal is to keep the pool rectangular in relation to the trees, perhaps to do it this way. . .

[Rote]

My first thought is to concur with Kharn, turning the pool 45 degrees gives a great deal of leeway. However, if the goal is to keep the pool rectangular in relation to the trees, perhaps to do it this way. . .

No, the goal was to keep the square shape of the pool and don't lose or move the trees.

[+Colibri]

Kharn got it right turn it 45° and you got a few more feet to go on each side. Check your bank for the 10ED.


Behind one of the doors is the prize
This one is also worth 10ED because it's a very known problem, that many mathematicians got wrong in the past, but now I think alot of people already know the correct answer.

You are at a gameshow on television, and you are presented with 3 doors. Behind one door is a brand new Ferarri (or an Audi, BMW, Mercedes, which ever you like most hehe). Behind the other two there's just a pile of hay.
First, you choose one door. The game show host then opens one of the doors that you didnt choose, behind which is a hay stack. There's now 2 closed doors - one with a car and the other with hay. You have a chance to change your mind and go for the other closed doors. Is it better to change your decision or not, or is it the same, and why?

(you need to explain why in order to collect the reward, if not it could have just been a lucky guess).

[kriptologist]

I say go for another door, you'll have a one in two chance of still winning the car, and if it's a stack of hay then you haven't really lost anything you didn't already have.

[Alegur]

Change your choice. Opening one of the doors changes the odds, so that you have something like a 66% chance of getting the right one, where your initial choice gave you only about a 33% chance of being right.

(I think I figured that like I meant to, I could be full of it, after all 99.4% of all statistics are made up )