You’re given 20 coins. The coins are of two kinds. Weights
of the first kind of coins are in the range [11 gr, 11.1 gr] and the other kind
weight in the range [10.6 gr, 10.7 gr]. Can you separate these coins using a
digital scale(which has a single pan) by 15 weighings? How?
When you say there's a digital scale, I assume it gives a readout of the total weight.
Weigh the coins in ten pairs.
If they're both light, the total will be 21.2 - 21.4
If they're both heavy, the total will be 22 - 22.2
If there's one of each, the total will be 21.6 - 21.8
Separate the pairs where both are heavy or both are light into their piles.
It may turn out that all the pairs are mixed. Weigh one of each pair. That will use up the other five weighings.