Since the wait for the legal dispute to be resolved is so maddening, I thought starting a new thread about riddles/problems might be fun (fun fun fun actually)!
Some of these riddles will naturally be more mathematically challenging, so I would like to state beforehand that there is absolutely no shame in not being able to solve some or all of them. In fact there is no shame in not caring at all!First riddle:
Answer to the first riddle:
What is the sum of the first n integers (starting from 1, not 0), i.e. show that
Here's the easiest way I know to show this:
First of all, let's denote the total sum by S, that is
S = 1 + 2 + 3 + ... + n - 2 + n - 1 + n.
We can rearrange the terms in backward order without altering the sum's value:
S = n + n - 1 + n - 2 + ... + 3 + 2 + 1.
Now, if we were to add those two we would obtain:
|S + S
|| (n + 1) + (n - 1 + 2) + ... + (2 + n - 1) + (1 + n)
|| (n + 1) + (n + 1) + ... + (n - 1) + (n - 1)
|| n * (n + 1)
Thus, we can isolate S:
S = n(n + 1) / 2
And that's it!
Answer to the second riddle:
What is the expected number of coin flips required to obtain your first 2 consecutive heads? for 3? for 4? Is there a patern?
Non-mathematical solution coming...
Answer to the third riddle:
You're standing in a rectangular cabin which has one window per wall. You stare through all 4 of them and realize you've been looking south every time. Where are you?
The north pole.
It would also be fun if people added riddles of their own as well. Will add more myself if the thread actually piques people's curiosity, if not... well... that's still 5 less minutes of waiting for me!
P.S. Sorry for the grammar...
EDIT: to add answers, to add riddles, and to better format the post...