Cards - Solution

Puzzle Location: Affymetrix
Next Puzzle: Balls

The first step to solving this puzzle is the recognition that the Texas flag indicates what sort of game the cards refer to: Texas Hold'em.



In Texas Hold'em, each player is dealt two cards face down, and all of the players share five community cards that are dealt face up. Each row of cards represents a set of these community cards.

Given a set of community cards, there is usually one pair of cards which gives the player the best possible hand (these cards are known as "the nuts"). Players who are lucky enough to receive this hand may bet their entire stake without risk as this hand is unbeatable. The key step in the solution of this puzzle determining which pair of cards gives a player the "nuts" for each set of community cards.
Community Cards
Q
6
6
10
10
A
K
9
5
4
3
3
3
J
Q
4
4
7
J
Q
5
2
8
9
A
3
6
7
8
9
9
10
5
2
7
K
K
5
4
A
10
J
8
6
2
A
2
J
Q
7
        
"Nuts"
10
10
2*
3*
3
4
4
6*
7*
10*
J*
8*
J*
2
3
9*
Q*
K
        
Hand
Four of a kind
Straight
Four of a kind
Four of a kind
Straight
Straight
Straight
Straight Flush
Straight
Flush


Note that the asterisks represent any suit, and that for two of the hands, only one card is relevant.

Converting the card values (ignoring suits) to numeric values according to standard conventions (A=1, 2=2, ..., Q=12, K=13), we get a sum for each set of "nuts".
"Nuts"
10
10
2*
3*
3
4
4
6*
7*
10*
J*
8*
J*
2
3
9*
Q*
K
        
Sum
20
5
3
8
13
21
19
5
21
13
        
Letter
T
E
C
H
M
U
S
E
U
M


This sends teams to the San Jose Tech Museum.