The coins currently in circulation in Britain are for 1p, 2p, 5p, 10p, 20p, 50p, 100p and 200p. When I gave one of each of these coins to Tom and Harry to share between them, each took two or more coins, with each person's coins' total value equal to a prime number of pence. No coins were left over.
I asked Harry whether his share was a specific number of coins that I mentioned. He said "no".
I then asked Harry whether he had the coin of a denomination I specified. He said "yes".
His two answers allowed me to determine the total of the value that Harry had taken. What was that value?
(In reply to Coincidence and binary searches
by Steve Herman)
One simple scheme would be to ask Harry if he has a 1p coin, and then
if he has a 200p coin, and if he has a 10p coin. This will always
be enough to determine his coins, no matter what his answer.