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 article's definition of not revealing information is a bit unclear, but if we understand it as Eve not knowing who holds any single card, your solution seems to work. At least assuming the following code is correct :)

import itertools import functools

for eve_card in range(7): cards_left = set(range(7)) cards_left.remove(eve_card)

    mod_to_cards = [[], [], [], [], [], [], []]

    for c in itertools.combinations(cards_left, 3):
        mod = sum(c) % 7
        mod_to_cards[mod].append(set(c))

    for combs in mod_to_cards:
        i = functools.reduce(lambda x, y: x.intersection(y), combs)
        if len(i) != 0:
           print("intersection", eve_card, combs, i)

        u = functools.reduce(lambda x, y: x.union(y), combs)
        if len(u) != 6:
           print("union", eve_card, combs, u)

Is the modulo required? Is just "The sum of my cards is x" sufficient?

Yes. For instance, if a player says the sum of their cards is 3, Eve immediately knows they have cards 0, 1 and 2.

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

Problem solved!