Does "the sum of my cards modulo 7 is [x]" work? It should let Bob know what the missing card is but I can't tell if it conveys sufficiently little information to Eve for it to count.
The advised reader could devise a solution using public / private key where:
- Alice communicates her public key
- Bob communicates his
- Alice encoders her cards with Bob’s public key
- Bob does the same<p>Problem solved!