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# Dueling cards

### #1

Posted 08 March 2014 - 06:26 AM

Moe and Joe had some time on their hands, so they played a simple game called "Dueling Cards."

In this game, each player has a deck of cards, shuffled and without jokers.

A hand consists of a single card taken from the top of each player's deck.

Suits and face values are both ranked. No two cards in a deck have the same rank.

A player wins the hand by holding a card that outranks the card of his opponent.

The bank pays 1 chip to the winner of a hand.

It's a simple game. No poker hands. No betting. Just high card wins.

After 52 hands the decks are re-shuffled, and play continues as long as desired.

Moe and Joe played through their decks 10 times, then stopped to see who won.

As they counted their chips Moe (a statistician) said, I wonder what the most likely winning score is.

Joe (a simpler person) replied, I wonder what the most likely combined score is.

I'm sure **Bushindo** can answer Moe's question.

I can't. So instead this puzzle asks Joe's question.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #2

Posted 08 March 2014 - 09:56 PM Best Answer

### #3

Posted 10 March 2014 - 09:48 PM

Does "combined score" mean the total number of chips Moe and Joe have together after 10 rounds?

If so, then the answer is 520, but where is the puzzle?

I'm sure that's not the right answer, so I'm not hiding it in the spoiler.

### #4

Posted 11 March 2014 - 12:33 AM

Does "combined score" mean the total number of chips Moe and Joe have together after 10 rounds?

If so, then the answer is 520, but where is the puzzle?

I'm sure that's not the right answer, so I'm not hiding it in the spoiler.

### #5

Posted 11 March 2014 - 08:30 PM

Does "combined score" mean the total number of chips Moe and Joe have together after 10 rounds?

If so, then the answer is 520, but where is the puzzle?

I'm sure that's not the right answer, so I'm not hiding it in the spoiler.

Spoiler for here's why

I knew I was missing something obvious.

### #6

Posted 11 March 2014 - 08:38 PM

Does "combined score" mean the total number of chips Moe and Joe have together after 10 rounds?

If so, then the answer is 520, but where is the puzzle?

I'm sure that's not the right answer, so I'm not hiding it in the spoiler.

Spoiler for here's why

I knew I was missing something obvious.

Spoiler for

I'll take slight credit for purposefully obfuscating that precise point (no two cards in **a** deck have ...) Heh.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

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