Leaderboard

A few puzzles posted in this forum have related to random triangles inside a circle. By evaluating nasty integrals, or by my preferred method, simulation, it can be shown, perhaps surprisingly, that triangles constructed from sets of three uniformly chosen points within a circle cover only about 7.388% of the circle's area on average. After looking at on the subject, I simulated 1 million triangles to determine the median area. It turns out to be about 5.335% of the circle's area. Read: a random triangle has a 50% chance of being smaller. If the distribution of random-triangle areas has a mean of about 7.4% and a median of about 5.3%, what value might you expect for the mode?

oh, and mensa is an ego thing. it costs to take an actual test to get into mensa (not an online one, something different. Im sure they monitor it or something so you cant cheat) the online thing is supposed to be an estimate of whether you could get in or not. they eggagerate so youll want to take the real test because you think you could actually make it, and they end up with your money. this is directed to king of pain and georgie

A while ago, about a clock with indistinguishable hour and minute hands and asked at what times of day, between the hours of noon and midnight, it was impossible to unambiguously determine the time. The hands moved continuously. This puzzle asks a related question. At what times of day, between the hours of noon and midnight, is it impossible to distinguish the hands of such a clock from those of its mirror image? Clearly noon is one of these times, but not in general thereafter -- since the clock's hands will move clockwise while the hands of its mirror image will move counterclockwise.

A pocket watch without numbers was rotated.. What is the time if the colored dials are the hour,second & minute hands of the watch?? Note: Idea from BMAD & Bonanova

Can you help me find the solution to the final question : I tried using alphabet substitution and it seems to work for the first 2..but I'm stuck in the final one.

Dear friend, Do you want to get rich quick? Just follow the instructions carefully below and you may never need to work again: 1. At the bottom of this email there are 8 names and addresses. Send $5 to the name at the top of this list. 2. Delete that name and add your own name and address at the bottom of the list. 3. Send this email to 5 new friends. If the process goes as planned, how much money would you make?