Trick of Mind

Chris posted his “Black or White” problem and laughed his evil laugh,thinking it would stump everyone and keep them guessing for days.His plan is foiled when BearSprite gives the right answer after a whole hour and 11 min.

Chris (angry and wanting payback) is chasing Bear thru the woods but can’t catch him as they both run at the same speed.After a blind turn,Bear falls into a circular pond and swims to the center.As he turns around and sees Chris standing at the perimeter (shaking his fist) he knows he is safe for the moment as Chris can”t swim.Bear knows the only chance for escape is to reach the perimeter of the pond and start running again with a bit of a lead on Chris.The problem is that Bear”s swimming speed is S and Chris”s running speed is 4S.

Who can come to the rescue and tell Bear what to do?

Three men A, B and C are captured by cannibals. They are tied to stakes. A can see B and C. B can only see C. C can’t see either A or B. They are then shown five hats. Three are black and two are white. The men are then blindfolded. A hat is put on each one’s head, the remaining two hats are hidden away and then the blindfolds are removed. They are told that if one of them can call out the colour of his own hat, they can all go free, otherwise they’ll really be in hot water. \they are not allowed to confer.

After a short time A calls out, “I don’t know my hat colour”. Soon B calls out, “I don’t know my hat colour either”. C thens called out the colour of his hat.

What colour is C’s hat?

A wire is tied to a normal bicycle pedal that is stationary at the bottom of its arc.  If someone pulls this wire backwards (while another person lightly holds the seat to keep the bike balanced), will the cycle move forward, backward or not at all?  Assume that the wheels don’t slip and that the bicycle doesn’t do a wheelie - bonus marks for justifying those assumptions.

Give reasons.

Some (n) people are standing in a queue. On average, how many of them can say that they are taller than everyone ahead of them?

NB The person at the front of the queue, can say that he is taller than everyone ahead of him.

At the end of the last century, General Eketahuna of Puzzlaria’s army was court martialed. The accusation was brought forth that a Puzzlarian soldier had killed an unarmed civilian in an opposing army. The General was considered responsible for the conduct of all his commands.
The defense had built its case on the possibility that a Puzzlarian civilian vigilante had killed the civilian. But as it happens, during the war all soldiers (80% of the populace) wore red uniforms, and all civilians (the remaining 20%) wore green. A single witness of unquestionable character had positively confirmed that the killer was in red. Other facts emerged that eliminated the possibility of a fake uniform, or tricks of the light.
It looked quite bad for General Eketahuna, until under cross examination it was revealed that the witness was somewhat colour blind. Carefully controlled tests determined that the witness could correctly tell red and green apart with only 85% accuracy.
The General smiled smugly, knowing that under court martial rules, he could only be convicted for his officers’ conduct if guilt was established with 95% certainty. The defense rested.
The prosecution’s lawyer, Slavy, stepped up and addressed the Puzzlarian Jury. How did Slavy win his case?

What is the probability that, in any breath that you take, that at least one molecule of it was exhaled by Archimedes in his last dying breath?

Assume that a breath contains 10^22 molecules and that the atmosphere contains 10^44 molecules.

The villain, Chris, in an old black and white movie is planning on blowing up the old silver mine the following morning with his arch-rival Slavy inside. Historically, his method has been to light the dynamite with an hour long fuse, and get out of town.
Lately, he’s noticed that a few minutes before he’s about to do his dastardly deed, our stalwart hero Cam arrives and saves the day.
Chris has developed a new plan. This time he’s going to use a forty-five minute fuse. With a little luck, the dynamite will dispose of both Slavy and Cam.
Unfortunately, Chris sent his comic relief henchman, Forsythe to buy his fuses. Forsythe came back with a half-dozen of the usual hour-long fuses.
The obvious solution would be to take three-quarters of one of the fuses, but Chris has observed that while the hour long fuses will always burn up in exactly one hour, their rate of burn isn’t constant. In fact, it isn’t uncommon for him to light a fuse and have it burn like crazy for the first fifty minutes, and then slow to a crawl during the last ten minutes. Which, oddly enough, is when Cam rides in to save the day.
Another possibility would be to light one fuse, wait fifteen minutes, then extinguish it. If only Chris had a watch, that would work.
How can Contemptible Chris carry out his dastardly deed – can you help him sort out a 45min fuse?

A lightbiker ‘A’ is riding at 252 milesph on his 1600 R. Four bikes are following it at 251.9999 milesh. Two lightbikes decide to overtake biker A, by attaining a speed over 251 milesph but under 261 milesph. Two of the four bikes are faulty, and will break down at 254 milesph. Given that the speed changes are final, what is the probability of LightBiker A winning?

Three traveling salesman (let’s call them Cam, Chris, and Slavy) from the Sharman Numple Company are on the road and find themselves in the same city.  Since Karl pays a per diem to his salesman the three decide to share one room and thereby each save some money for themselves.

They register at the front desk and are told the price for the one night is $30.  Perfect!  They each cough up a crisp $10 bill and pay for the room.

Later that evening the manager is at the front desk and asks the clerk how things are going.  The clerk replies that three salesmen checked in and he charged them $30 for the room.  The manager yells uncontrollably at the clerk for his mistake.  “You know if I’ve told you once I’ve told you 1000 times that salesmen from the Sharman Numple Company get the discounted rate of $25 per night! Now get up to their room and make things right!”

The clerk, let’s call him Forsythe303, takes five one dollar bills from the cash register and heads up to the room.  On his way up and out of the sight of the manager, he puts $2 into his own pocket.  He knows that there is no way to even divide $5 by three salesmen and besides that, if they are each getting a refund, they won’t mind.  Especially since he already knows they are cheating Karl by sharing one room.

Upon arriving at their door, Forsythe303 explains he made a mistake and apologizes.  He tells them the hotel offers a discount to salesmen from Sharman and he hands over the three one dollar bills.  The salemen naturally say, “that’s alright, think nothing of it.”  They are happy to get a partial refund.

Now here’s where it gets tricky.  Each salesman originally paid $10 but each got a $1 refund.  Three salesman paying $9 each for a total of $27.  Right?  Right!  Forsythe303 has $2 in his pocket.  Right?  Right!  $27 plus $2 equals $29 dollars.  Where is the 30th dollar?

How many queens can you place on a chess board so that none of them are able to attack any of the others? Can you prove that it is impossible to place more than your number? (Queens attack any distance vertically, horizontally, or diagonally)