BMAD

quick question for clarification. Will the host participate in this too or is there only four participants?

That makes sense! Thank you.

also, is it that we can't move the same number consecutively or is it that we can't do the same number more than once?

I understand that to go from [1,2,5,3,4] to [1,5,3,4,2] can be easily achieved by moving the 2 to the rear but how does one then go to [4,2,1,5,3]? Can we slide two numbers at once?

Assume that the game in is the same. But this time, you are the dealer with control of building the deck. what would be the most profitable orientation of the cards on behalf of the 'house'.

A deck of 26 red and 26 black cards is shuffled into random order and placed face down. Then the cards are turned up one by one and observed by a guesser. He gets one guess: At a moment of his choice he may assert that the next card will turn up red. After this card is turned up the game ends and he wins if his assertion was correct, loses otherwise. And if he doesn't guess at all by the time all cards have been dealt, he loses by default. He receives 2x(x-1) dollars for a correct guess but loses (n(n-1)) + 2x(x-1) dollars for an incorrect guess; x is the number of cards faced down (unseen by the guesser) and n is the number of cards shown to the guesser. How should the guesser play the game? Does the strategy change if they were to play the game 1000 times?

Consider computing the product of two complex numbers (a + bi) and (c + di). By foiling the polynomials as we learned in grade school. We get: a + bi c + di ---------- adi - bd ca + cbi ---------------- (ca - bd) + (ad + cb)i Note that this standard method uses 4 multiplications and 2 additions to compute the product. (The plus sign in between (ca - bd) and (ad + cb)i does not count as an addition. Think of a complex number as simply a 2-tuple.) It is actually possible to compute this complex product using only 3 multiplications and 3 additions. From a logic design perspective, this is preferable since multiplications are more expensive to implement than additions. Can you figure out how to do this?

Two astronauts are standing on a spinning space station shaped like a disk. They are the same radial distance away from the disk's center, and standing opposite to each other across from the center (e.g., if you draw a line connecting the two astronauts, the line crosses the disk's center.) One astronaut wants to toss a wrench to the other. Among the infinitude of trajectories which will accomplish this goal, characterize one of the trajectories without writing a single equation.

But remember, I do not need a line. I just want the vertices that make the desired shapes. There is no request to actually connect the vertices.

Be nice friends. This is a math forum not a drama forum. I saw and took no offense in either post.

Why would you need a straight edge? I just want points.

Yes. I mean combinations.

Position five relative to?

6 friends are sitting in a circle whom you have been observing playing the game called 'spin the bottle'. They invite you to play as well. Being a good sport, you agree to play. You happen to notice however that it is HIlga's turn and you would rather not kiss Hilga. You have also noticed that the bottle when spun with the left hand has a tendency to stop on a person an even distance away (e.g. the second, fourth, sixth person from her) and when spun with the right hand will land on a multiple of 3 distance away from HIlga. Currently the bottle is pointing directly across from Hilga but if it were to land on herself she would immediately spin it again from that position, switching hands in the process. You have no idea which hand she will use first nor do you know which way rotation she will place on the bottle [clockwise or counter-clockwise]. Where should you sit?

At a movie theater, the manager announces that a free ticket will be given to the first person in line whose birthday is the same as someone in line who has already bought a ticket. You have the option of getting in line at any time. Assuming that you don't know anyone else's birthday, and that birthdays are uniformly distributed throughout a 365 day year, what position in line gives you the best chance of being the first duplicate birthday?

Using positive integers only, how many ways can can the sum of 271 be found?

Using only a compass to make circles of any size you choose, find a method to locate five points that if connected would make a regular pentagon. Is it possible to make a heptagon using a compass and circles?

If you ask me if there exists another world [after death], if I thought that there exists another world, would I declare that to you? I don't think so. I don't think in that way. I don't think otherwise. I don't think not. I don't think not not. If you asked me if there isn't another world... both is and isn't... neither is nor isn't... if there are beings who transmigrate... if there aren't... both are and aren't... neither are nor aren't... if the Tathagata exists after death... doesn't... both... neither exists nor exists after death, would I declare that to you? I don't think so. I don't think in that way. I don't think otherwise. I don't think not. I don't think not not. --I do not recall this famous quote's author unfortunately.

hi

You have an unlimited supply of 7 and 11 pound weights. You also have a 5 pound potato. Can you weigh the potato on a balance scale? What about a 9 pound potato?

Suppose the point on a line segment is in a one to one correspondance relationship with a line. Both possess infinite points and so should fullly map onto each other however the line segment is of finite length while the line is of infinite length.

Assume we know nothing of Pi's actual value. Apparently, we think it is some random number generated by a calculator every time the Pi button is pressed. All we know that is 2*Radius*Pi is the circumference of a circle and pi*radius*radius is area. Use a unit circle to prove that Pi is >3 and <4.

Is it possible to find six points on a square lattice that form the vertices of a regular hexagon?