BMAD

Mooli found the answer I was looking for. Well done!

The rotation speeds change between any overlapping pair or when all three overlap?

Five pieces are randomly selected from a standard chess set. If it is known that at least one of these pieces is a pawn, what is the probability that at least two of these five pieces are white pawns?

You and your friend are told that there are N cards, each are numbered from 1 to N. You will randomly select 6 cards. Using the perfect coding system which you had set with your friend previously, you will select one card and transfer the other five to your friend. By just examining the order of these numbered five cards, your friend will be able to know the card youve selected. What can be the maximum value for N?

Hmmm. I did not consider a single coin

N lamps are set in a circle, and for each integer M you have a tool that can toggle the state (on/off) of any set of M consecutive lamps. Find a possible N which satisfies the following statements: The sum of its digits is less than 10. By applying the tool for M=105 several times, we can toggle a single lamp. If we remove one lamp and start from a random initial setting for the remaining N-1 lamps, the probability that there exists a way to apply the tool for M=32 several times and switch all the lamps off is positive and less than 0.0011%.

In a certain country 1/2 of 5 = 3. If the same proportion holds, what is the value of 1/3 of 10?

My interpretation is along the lines of Joe student

Why?

agreed

Try out (or imagine) the following simple game with a friend: You each toss a fair coin as many times as necessary to get a required sequence. Your required sequence is H T H Your friend's required sequence is H T T. Do this several times and each time write down the number of tosses you needed The winner is the player whose average number of tosses is the lowest. For example: Game 1: You toss: H T T H T H Friend tosses: H T H H H T H H T T Your 'score' is 6 and your friend's is 10 Game 2: You toss: T T H T T H H T H Friend tosses: T T H H T H T T Your 'score' is 9 and your friend's is 8 Game 3: You toss: T T H H T H Friend tosses: H H T H T T You both 'score' 6. At this point your average is 7 and your friend's average is 8. The conundrum: Assuming you played the game many times, which of the following outcomes would you expect? A) You win (i.e. your average is lower than your friend's). B) Your friend wins (your average is higher than your friend's). C) You tie (your average is about the same)

If you randomly cut a stick (straight cuts) into four pieces, what is the probability that the resulting pieces will make a quadrilateral? Pentagon? Octagon?

Suppose John tosses a coin 250 times and Eric tosses a coin 251 times, what is the probability that john's coin has more heads than Eric? What is the probability that Eric has more heads than John?

@joshuagenes that explains about those of the line of eve but what of those who are from Lilith?

The gunslinger series by Stephen King

I believe Pickett has it

I am unsure about neat but since these are integers

That is a mouthful

Correcting an error in the simulation program, The probability that a random triangle inside an equilateral triangle covers its centroid is 0.24543 ... The average size of a random triangle inside any triangle is 1/12. I am assuming you mean the mean average.

Imagine you have a special keyboard with the following keys: 1. A 2. Ctrl+A 3. Ctrl+C 4. Ctrl+V where CTRL+A, CTRL+C, CTRL+V each acts as one function key for “Select All”, “Copy”, and “Paste” operations respectively. If you can only press the keyboard for N times (with the above four keys), please write a program to produce maximum numbers of A. If possible, please also print out the sequence of keys. That is to say, the input parameter is N (No. of keys that you can press), the output is M (No. of As that you can produce). Example:- For N = 8 the answer is M = 9, where S = { A, A, A, CTRL+A, CTRL+C, CTRL+V, CTRL+V, CTRL+V }. For N = 9 the answer is M = 12, where S = { A, A, A, CTRL+A, CTRL+C, CTRL+V, CTRL+V, CTRL+V, CTRL+V }.

Again...why so many players?

This is a simple game like Pachinko and in a similar vein as my "coin with a conscience" problem. You insert money into the machine at one metal ball per 10cents. The balls drop one at a time onto discs. The first ball drops and lands on a disc and then rolls and lands on the next disc, and then falls on two more (for a total of 4 discs). If after landing on the fourth disc, the ball rolls off to the left, you get 20cents. if the ball rolls off to the right, you earn nothing. After inserting your money, you choose whether the 1st ball should aim for the left part of the first disc or the right part of the first disc (and the ball will always go down that particular side). Once a ball goes down a particular side, the rest of the discs are rigged to bias the odds the ball falls the other way by a change of 5%. For example--with 1 ball aim for right side, disc 1--(goes down right side), disc2-- 52.5% (50% * 1.05 = 52.5) likely to fall down left, disc 3-- 52.5% likely to fall down left, disc 4-- 52.5% likely to fall down left ball reaches disc2 say it falls down the left side, 49.875% likely to fall down the right side of disc 3, 49.875% likely to fall down the right side of disc 4 ball reaches disc3, say it falls down the left side of disc3, 52.36875% chance it will fall down the right of disc4 say the ball rolls off the right side of disc4....darn, i lost 10cents. Can you make money playing this game in the long run? If so, how should you play it? If not, why not?

Both are well said but there seems to be disagreement as to the knight moves; however the balancing issue that BobbyGo references may be an issue resolved by Bonanova's equation.

Consider a an infinite chessboard. How many squares can a knight reach after precisely n moves? How about a bishop?