If there are k symbols in a Dobble game card, how many comparisons are needed at the maximum?
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In the Dobble card game there is a deck of 55 cards. Each of them has 8 symbols on it. There is a total of 50 different symbols and each two cards have one and only one in common.
I am wondering, given a total number of symbols N and a number of symbols on each card K, how do you find the biggest number of cards such that:
on each of those cards there are exactly K of the N symbols,
every two cards have one and only one symbol in common.
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