Math - not an April fool's joke

-  2690  -  This is not an April Fool’s joke.  It is just math.  I will send the answers upon request.
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-------------------  2690  -  How many spades is Nathan holding in his left hand?
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-  Nathan got his caste off today.  Congratulations, but, it is raining cats and dogs.  So, we are stuck inside and can’t play baseball.  So, Nathan got out a deck of cards.  He picked up 7 black card and 6 red cards in his left hand.  He noted that he had  twice as many hearts as clubs and twice as many diamonds as hearts.  How many spades did Nathan have in his new hand?
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-  Remember, if you are smart enough to be a mathematician and not a politician then you must resolve yourself to be governed by someone dumber than you.
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-  Please send answers or request answers
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-  Please rate your like ability for puzzles, I have hundreds more.
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-  Nathan is playing games again,  he is into this stuff.
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-  He put some coins in his left pocket.
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-  He put some coins in his right pocket.
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-  He figured that the square of the number of coins in his right pocket plus the cube of the number of coins in his left pocket works out to be 368.
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-  He also figured out the if he cubed the number of coins in his right pocket plus the square of the number of coins in his left pocket he would get a smaller number, 174.
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- You have enough information to determine how many coins he has in each pocket.
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-  April 1, 2020                         1432                                                2690               
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 ---------------------   Wednesday, April 1, 2020  -------------------------
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