find the counterfeit by minimum number of weighings

Hi, I got a question, can anyone please help me?

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 the weight of a genuine $1 coin and you are also told that each counterfeit coin weighs 1 gram more than it should. You may weigh the coins on a pointer scale (ie not a set of scales with two dishes). What is the smallest number of weighings needed to determine which stack is counterfeit?

My current answer is 4 times. I will seperate 10 stacks become 4, 4, 2.

Then weigh 4, and 4, but not 2. If two 4 stacks are equal, then counterfeit is in 2.

If not, the heavier 4 will be the one contains counterfeit.

Then, seperate this heavier one become 2 and 2. Only weigh one of them, if yes, this one contains counterfeit, if not, the other one contains.

Then weigh only 1 of 2 for the one contains counterfeit, that will find the counterfeit.

So totally I weighed 4 times, will it be possible even less than 4? Thanks a lot.