Originally Posted by

**Wilmer** Ok; then your problem should be worded this way:

You have 10 stacks of coins, each consisting of 10 $1 coins.

One entire stack is counterfeit, but you don't know which one.

You do know that the weight of a genuine $1 coin is 10 grams. ***

And you are also told that each counterfeit coin weighs 11 grams.

You may weigh the coins on a pointer scale (ie a scale that shows the actual weight).

What is the smallest number of weighings needed to determine which stack is counterfeit?

*** I used 10, but could be any weight you choose; does not matter since counterfeit is 1 more.

Answer: ONLY one weighing is necessary.

Number the stacks 1 to 10.

Take 1 from stack1, 2 from stack2, ......,8 from stack8, 9 from stack9 (none from stack10).

So you have 45 coins on scale (1+2+...+8+9 = 45).

If weight = 450 then counterfeit = stack10

If weight = 451 then counterfeit = stack1

If weight = 452 then counterfeit = stack2

.....

If weight = 458 then counterfeit = stack8

If weight = 459 then counterfeit = stack9

Got that?