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.