Problem solving

Question

In a group of nine coins which are identical in appearance, eight weigh the same and one is heavier than the rest. using a balance scale, what is the minimum number of balancings needed to identify the heavy coin ? show all your work and state which strategy, or strategies you use to solve the problem. 

Answer 1

Hi Aman, the answer is 2. Start by separating the coins into three stacks of three each. Then weigh any two of the stacks.

 

Step 1:

If the two stacks are the same, the heavier coin is in the remaining stack, the one not weighed. Go to step 2.

 

If one of the two stacks is heavier than the other one, the heavier coin is in the heavier stack. Go to step 3.

 

Step 2:

Weigh any two of the unweighed coins from the stack that has not been weighed. If the coins are the same, the one not being weighed is the heavier coin. If the coins are not the same, pick the heavier one.

 

Done in two uses of the balance scale.

 

Step 3:

Weigh two coins from the heavier stack from step 1. If the coins are the same, the one not being weighed is the heavier coin. If the coins are not the same, pick the heavier one.

 

Done in two uses of the balance scale.

 

In either case, you will use the balance scale two times.

 

Questions?