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So here's the problem

"There are 49 cards here. Can you figure out what the seven facedown cards are and what position they're in?"

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I have tried about everything in my math tool belt to try and solve this.

I tried to see if each suit had a unique constant attached to it and used the four full columns. That worked but falls apart when applied to unknown cards.

If clubs = -125 spades = 415 diamonds = -234 hearts = 64 the four known columns all add up to 194.

I highly doubt it's this complicated but I want to show I've exhausted a large amount of other more trivial attempts and am at my wits end.

Any ideas would be much appreciated.

if it helps here is A' if A is the face up cards. {Ace of hearts, 2 of spades, 7 of hearts, 7 of diamonds, 9 of diamonds, 10 of spades, J of spades, Q of clubs, Q of hearts, and K of hearts} (cards that are either flipped face down or not on the board.)

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