Imagine you are in a game show where there are three doors, behind one of which there is a prize. The host asks you to choose a door, then opens another (empty) and gives you the choice to switch to the last door. Do you keep the same door, or switch?
can’t tell if this is a genuine question or not, but from a statistical standpoint, you want to switch. Your first choice is choosing between three, so that choice has a 1/3 chance to succeed. After one door is revealed empty, changing door means that you now have a ½ chance (staying the same does not change the odds because nothing about your choice is changing).
Anyways my house is full of traps
After changing doors, the host reveals that behind the door you chose, there is a room full of starving lions that have not eaten in 100 days. Behind the door you originally chose, there are men with axes who want to kill you.
The host takes you into an elevator. The elevator is moving downwards at a speed of 12m/s. Another elevator is moving up at 15m/s, but stops after 3.2s. Assuming the distance between the elevators at the start is 3000m, at what distance from the doors floor will your elevator be when it crosses the other elevator?
(I should clarify the men with axes don’t kill you because you haven't opened the door. Yet. Maybe that's foreshadowing step 8.)
Why would I go into the elevator? Those lions are long dead, which means that I chose the best door (at least I get their bones or something idk), this elevator business makes no sense. But if the host is insisting I solve a math problem, then I will. The cars should pass at 246 seconds from start, assuming constant rates, at which point it is statistically the best survival option to jump to the faulty car and get myself away from this insane show host.
Please don’t leave, I haven’t even introduced Hilbert's Hotel, the horse or the Sleeping Beauty problem yet :(
And also if you successfully complete the quiz you gain unlimited power, in a different universe.
the horse’s name is Friday
I would ask the door which door the other door would say the prize is behind
Actually here’s a better solution than my earlier one
Simply state “if this sentence is true, whichever door I pick has the prize behind it”. Call the sentence X. If X is false, then by principle of explosion any sentence of form “if X, then Y” is true. However, X itself is of this form, thus X is both false and true at the same time. Therefore, X must be true. And since it is true, whichever door you pick must have the prize behind it. This works 100% of the time regardless of if you keep or switch.
(relevant search term for more information: Curry's paradox)
WHAT
I love Curry’s paradox it is my favorite paradox in all of mathematics
That is absolutely mind-numbing