[Edit] As pointed out by longway, there's a hole in this.
My assumptions:
Method:
Divide the 100 coins into 2 groups A and B, each comprises 49 coins. The remaining 2 coins are labelled C and D.
- Weight A and B.
1.1 A > B (which also handles symmetrically B > A)
Divide A into 24 + 24 + 1 coins, and weigh 24 vs 24.
1.1.1 If the two sides are equal, all of them are genuine.
1.1.2 Otherwise the heavier side contains all genuine coins.
1.2 A = B
Divide A into 24 + 25 coins, add C to the 24 side, and weigh 25 vs 25. Call the side containing C the C-side.
1.2.1 If the C side is heavier, then C is genuine.
1.2.2 If the C side is equal to the other side, then C side minus C are all genuine.
1.2.3 If the C side is lighter, then the other side contains all genuine coins.
Explanation:
Divide the 100 coins into 2 groups A and B, each of 49 coins, and label the remaining 2 coins as C and D.
- Weight A and B.
1.1 A > B, it means that B has more fake coins than A. Clearly this means that A has either 0 or 1 fake coins.
Divide A into 24 + 24 + 1 coin, and weigh 24 coins against the other 24 coins.
1.1.1 If they are equal, then they must all be genuine since there's at most one fake coin.
1.1.2 If they aren't equal, the heavier side contains all genuine coins.
The case where B > A is symmetric.
1.2 A = B, it means that A and B have same number of fake coins. This number could be 1 or 2.
Divide A into 24 + 25 coins, and add C to the 24 portion, and weigh these 25 coins against the other 25.
If A and B both have 1 fake coin only, that means both C and D are fake.
If A and B both have 2 fake coins, that means both C and D are genuine.
That means
if A has 1 fake coin, then the C side is
- equal to the other side when C-side minus C are all genuine coins, and the other side contains one fake coin.
- lighter than the other side when C-side contains the other fake coin as well. In this case the other side contains genuine coins.
if A has 2 fake coins, then the C side is
- lighter than the other side when both fake coins are on the C-side. In this case the other side contains genuine coins.
- heavier than the other side when some fake coins are on the other side. In this case, C must be genuine anyway since A has 2 fake coins.
So
- if the C side is heavier, then C is genuine.
- if the C side is equal to the other side, then C side minus C are all genuine coins.
- if the C side is lighter, then the other side contains all genuine coins.