SOLUTION: Six coins are lying in a triangle. You have to move some coins to place them in a circle as you can see in the second picture. How many coins must be moved at least?

Algebra ->  Average -> SOLUTION: Six coins are lying in a triangle. You have to move some coins to place them in a circle as you can see in the second picture. How many coins must be moved at least?       Log On


   

Question 1135387: Six coins are lying in a triangle. You have to move
some coins to place them in a circle as you can see in the
second picture. How many coins must be moved at
least?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Moving 2 coins can make a circle; moving only 1 can't.

Think of the 6 coins when they are in a circle as the vertices of a regular hexagon.

The problem then becomes determining the minimum number of coins that have to be moved from the original triangular array to accomplish that.

Then the problem is to find the largest number of the 6 coins in the original array that do NOT need to be moved to become vertices of a regular hexagon.

A look at the original array shows that 4 of the 6 coins can stay where they are. For example....

        1                    6   1

      2   3        -->     2        3

    4   5   6                4   5