# Counting all the hearts

The Arthur family ( Henrik, Olga, Heather and Kristophe) are playing Bridge at the dining table with a standard deck of cards.

Taking into account every possibility

How many hearts are at that table?

First,

there are $$4$$ human hearts.

Then,

Considering this image of standard playing cards:
The cards have $$2$$ hearts on each card next to the name of the card, each face card has $$2$$ additional hearts in the art, and every other card has its number of hearts, totaling $$2\cdot13+3\cdot2+(1+2+\dots+10)=26+6+55=87.$$

Finally,

The family's names contain letters that form the word heart. We will use Dr Xorile's suggestion to count the total number of ways to form heart using different instances of the letters in their names. If we take their full names: Henrik Arthur, Olga Arthur, Heather Arthur, and Kristophe Arthur, we count $$8$$ H's, $$4$$ E's, $$6$$ A's, $$11$$ R's, and $$6$$ T's, giving $$8\cdot4\cdot6\cdot11\cdot6=12672.$$

$$4+87+12672=12763$$.

• You have to take into account every possibility: what if one of them is a timelord? – Arnaud Mortier Mar 11 at 16:28
• Do the people portrayed in face cards have hearts? (I say no, they are mere abstract sketches of people. Perhaps DEEM thinks otherwise.) – Gareth McCaughan Mar 11 at 16:38
• @GarethMcCaughan I was thinking the same. After all, the King cannot still have a heart with that sword stuck in his head for so long. – noedne Mar 11 at 16:40
• At some point we might begin to suspect that the Arthurs are octupuses. – noedne Mar 11 at 16:52
• Every possibility? Well, for all we know there's another part of the table piled high with dozens of other packs of cards... – Gareth McCaughan Mar 11 at 17:16

Starting with noedne's analysis of

87 hearts

from the card deck alone. We also have:

four (I assume) humans, that have one heart each... except that the two women could be pregnant (take into account every possibility!), and with humans twinning is reasonable, but triplets are pretty rare, so I would say up to 8 human hearts.

Oops, almost forgot to look at:

The text itself! The Arthur family has a cleverly hidden heart, and there are enough letters in the other names for 2 more, adding these to the human and card hearts are 87+8+3 for a grand total of 98 hearts. I think this is a stretch, but the fact that there are 52 cards in a deck also looks like a heart(), so that would make 99.

Or if you want to be absolutely ridiculous:

Octuplets have been born a few times, so you could have 4+8+8=20 human hearts for a grand total of 110, but at that rate do you count multiple births higher than eight as long as they can have a beating heart in the womb? That's why I consider this a ridiculous option.

Unlimited.

How many decks are represented?

How many hearts did those ladies steal?

"Every possibility" might consider the vermin hiding under the table or the table itself could have an array of hearts. Heart wood? Carved hearts?

The table cloth could have hearts on it. The tableware or China, as well.

The core principles, here, are that hearts of various sorts abound and not narrowing the field unbounds the total.

• agreed. That's pretty much what my answer amounted to. – NH. Mar 12 at 15:05
• Oh, agreed. Just think this was a touch more explicit. (That, and I couldn't resist the pun.) – The Nate Mar 12 at 19:03