Brain Teasers & Puzzles
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A specialist Gardener asked by a Mathematics professor to plant four trees that are all equidistant from each other. How do he place the trees?
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Jacob and John are competing for the same girl. After years of battling, both decide to settle it by tossing a coin.
John produces a coin, but Jacob doesn’t happen to have one on him. Jacob is sure that the coin John has produced is loaded, i.e. it will come up with heads more than 50% of the time on average.
How do Jacob arrange a fair contest, based purely on chance and not skill, by flipping this coin?
Variation: (COIN BIASING) Jacob and John are competing for the same girl, and decide to settle it with a coin toss. John has known the girl longer than Jacob have, so Jacob agree that it is fair for him to have a chance of winning equal to P, where P > 0.5. However, Jacob only have a fair coin. How can you conduct this contest such that the biased probability is manifested? What is the average number of coin flips needed to determine a winner?
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Pairs of primes numbers separated by a single number are called prime pairs like 17 and 19. Prove that the number between a prime pair is always divisible by 6 (assuming both numbers in the pair are greater than 6).
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You are a contestant on the Jacob game show. Three closed doors are shown before you. Behind one of these doors is a Bike; behind the other two are Goats. The contestant does not know where is the bike, but Jacob does.
The contestant picks a door and Jacob opens one of the remaining doors, one he knows doesn’t hide the bike. If the contestant has already chosen the correct door, Jacob is equally likely to open either of the two remaining doors.
After Jacob has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the bike if he stays with his first choice? What if he decides to switch?
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A snail is at the bottom of a well that is 20 meters in depth. Every day the snail climbs 5 meters upwards, but at night it slides 4 meters back downwards. How many days must elapse till the snail reaches the top of the well?
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On a circular path two person are walking in anti direction. How many times they will cross each other in one full round ?
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An analog clock showing 3:15. What is the angle between the minute hand and hour hand?
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Jacob is hanging out on a heavily forested island that is really narrow: it is a narrow strip of land that is Eight miles long. One End of the strip is A, and the other end B. A fire has started at A and the fire is moving toward B at the rate of 1 mph. at the same time, there is a 2 mph wind blowing in the direction from A toward B. what can Jacob do to save himself. Assume that Jacob can’t swim and there are no boats, jet-copters, teleportation devices, etc.. (if he does nothing, Jacob will be toast after at most 8 hours, since 8 miles / 1 mph = 8 hours)
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