How many times I have to use a scale

[brucejin]

There are 64 identical-looking coins, one of which is slightly heavier than the others. A balance scale can be used to show which one of two groups of coins is heavier or that the two groups weigh the same.
What is the minimum number of uses of the balance scale that is guaranteed to determine which of the coins is the heavier one?

My answer:
After 1 use of the scale, I have 32 coins that contains that heavier coin;
After 2 uses of the scale, I have 16 coins that contains that heavier coin;
After 3 uses of the scale, I have 8 coins that contains that heavier coin;
After 4 uses of the scale, I have 4 coins that contains that heavier coin;
After 5 uses of the scale, I have 2 coins that contains that heavier coin;
Then use the scale 1 more time to decide which of the 2 is heavier.

Total use of scale: 6.

Am I right.

My book says the answer is 4.

 

[Denis]

Try again with 21 against 21 to start.
If one side is heavier, then you're already down to 21.
If both sides equal, then heavy is in the other 22.

Carry on similarly....

 

[brucejin]

Thanks Denis;

I never thought there was such a better way.
Is this 3-group way an universal way od dealing with this kind of problems?

Thanks

 

[Denis]

Thanks Denis;
I never thought there was such a better way.
Is this 3-group way an universal way od dealing with this kind of problems?
Thanks

Yes.

Next to try would be 1/4 : 1/4, or 16 against 16 in your example.
If even (worst case), then repeat with the other 32:
so you're down to 16 after 2 tries: NOT as good as 22 after 1 try.