First weight 8 against 8 coins, leaving 11 coins on the side. The variation where a set of 8 coins weighs less than the other one is staightforward. The lighter group of 8 can not have more than 1 heavy coin. Split that set into 4 and 4, weigh them against one another, and the lighter set of 4 is standard. Should they weigh the same -- all 8 are standard.

The case where both sets of 8 weight the same is more difficult. There are 3 possibilites: each of the equal sets of 8 have 2 doubly wrapped coins, or they each have one, or both have zero coins. Correspondingly, the set of 11 on the side has zero, 2, or 4 heavy coins.

Lets name one set of 8 W1, the other set of 8 -- W2, and the set of 11 coins left on the side -- S11.

Then the second weighting should be as follows:

Leave W1 in the pan and put 4 more coins from W2 into the same pan. Lets call those 4 -- W2(4). Put one coin from W2 into the other pan, lets call it W2(1). Add the entire S11 into that pan. That leaves 3 coins from W2 on the side. Lets call them W2(3).

Thus after the second weighting of 12 coins against 12, the solution is as follows:

1. W1 + W2(4) > (weighs more than) W2(1) + S11, then the entire S11 is guarantied to be standard.

2. W1 + W2(4) = W2(1) + S11, then W2(1) + W2(3) have to be standard.

3. W1 + W2(4) < W2(1) + S11, then W2(4) must have standard coins only.

Here is the reasoning behind that solution:

1, If S11 contains standard coins only, its side of the balance should always be lighter. That is because in that case W1 contains 2 doubly wrapped coins and the balance side of S11 + W2(1) can at most have one. Also, this is the only case when that side could be lighter because in the other cases S11 contains either 2 or 4 heavy coins. Thus when S11 + W2(1) is lighter, S11 must be all standard coins.

2. If S11 has 2 doubly wrapped coins then

a). to balance the scale W1 + W2(4) must have the remaining 2 heavy coins, which leaves W2(1) + W2(3) standard.

b). when S11 + W2(1) side is heavier, knowing that W1 contains 1 heavy coin, leaves W2(4) standard.

3. Finally, when S11 contains all 4 doubly wrapped coins making its side of balance heavier, we can safely pick W2(4) as a set of standard coins.