Thursday, January 31, 2013

Puzzle 21: Complete one round.

Puzzle 21: There is an round island with one Air base. You have supply of "n" air planes. You need to make one plane should complete the circle boundary with the following constraints:

  1. One plane can travel only half of the island boundary with one full tank.
  2. There is no way a plane can land in between.
  3. You can transfer the fuel from one plane to other in air only, but make sure that plane which is transferring the fuel from one plane to other should have sufficient fuel to come back to the base.
  4. Planes can fly in clockwise or anti-clockwise direction.
  5. Make sure no plane crash due to any reason.

Solution: This can be solved by using 6 planes as follows:

Now as per given data a plane can try with one full tank from A to B max.
Refer the following table to get idea how things work with multiple planes.
To make it easy, let's consider all planes need 4 units of fuel to full the tank.
So fuel required to reach to B from A (Clockwise direction) will be 1 Unit.

So from the above table, it's clear that by using 3 planes we can reach from A to G in clockwise direction.
Similarly by applying symmetry we can make one more plane to reach G in anti-clockwise direction  by using 3 planes used in the same manner.

So the full tank plane, let's say Plane 6 reach with full tank at position G then plane 6 will transfer 2 units fuel to Plane 1 and both can come back to base safely.

Monday, October 29, 2012

Puzzle 20: Survivors Issue

Puzzle 20: A group of Englishmen are travelling on a German plane, piloted by an Norwegian, bound for Finland. If the plane was to crash in Sweden, where would the survivors be buried?
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Puzzle 19: 1 sheep for 3 animals

Puzzle 19: A lion can consume one sheep in two hours, a wolf can consume three sheep in eight hours and a hyena can consume one sheep in eight hours. If all of the animals were in a cage and were given a sheep, how long would it take them to consume it?

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Puzzle 18: Misfortune Clock

Puzzle 18: You have the misfortune to own an unreliable clock. This one loses exactly 20 minutes every hour. It is now showing 4:00am and you know that is was correct at midnight, when you set it. The clock stopped 4 hours ago, what is the correct time now?

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Friday, October 26, 2012

Puzzle 17: Top 3 among 25 horses

Puzzle 17: You have 25 horses. When they race, each horse runs at a different, constant pace. A horse will always run at the same pace no matter how many times it races.
You want to figure out which are your 3 fastest horses. You are allowed to race at most 5 horses against each other at a time. You don't have a stopwatch so all you can learn from each race is which order the horses finish in.
What is the least number of races you can conduct to figure out which 3 horses are fastest?

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Puzzle 16: 10 Cigarette Butts

Puzzle 16: Bruce is an inmate at a large prison, and like most of the other prisoners, he smokes cigarettes. During his time in the prison, Bruce finds that if he has 3 cigarette butts, he can cram them together and turn them into 1 full cigarette. Whenever he smokes a cigarette, it turns into a cigarette butt.
One day, Bruce is in his cell talking to one of his cellmates, Steve.
"I really want to smoke 5 cigarettes today, but all I have are these 10 cigarette butts," Bruce tells Steve. "I'm not sure that will be enough."
"Why don't you borrow some of Tom's cigarette butts?" asks Steve, pointing over to a small pile of cigarette butts on the bed of their third cellmate, Tom, who is out for the day on a community service project.
"I can't," Bruce says. "Tom always counts exactly how many cigarette butts are in his pile, and he'd probably kill me if he noticed that I had taken any."
However, after thinking for a while, Bruce figures out a way that he can smoke 5 cigarettes without angering Tom. What is his plan?

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Thursday, October 25, 2012

Puzzle 15: Racing position.

Puzzle 15: In the final stretch of a road race, you pass the 2nd-place runner right before crossing the finish line. What place do you finish in?
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