## Tuesday, February 12, 2019

### card puzzles

In these puzzles, each suit is given a value. The value of the card is the face value of the card multiplied by its suit value. Aces may be low (face value 1) or high (face value 11).  Face cards (Jack, Queen, King) have face value 10. Other cards have face value equal to their number.

Puzzle 1 (warm up)
In this puzzle, black cards (spades and clubs) have suit value 2 and red cards (diamonds and hearts) have suit value 3. What is the card value of each card shown?

Puzzle 2 (introducing sets)
When cards are put next to each other, we add their values. In this puzzle, spades have suit value 1, clubs have suit value 2, diamonds have suit value 3, and hearts a have suit value 4. Aces are high. What is the total value of each set?

Puzzle 3
In this puzzle, spades are worth 2. Each set is worth 20. What are the values of the other suits?

Puzzle 4
In this puzzle, Aces are low. The value of each set is shown below it. What is the value of each suit?

Puzzle 5
In this puzzle, Aces are high. The value of each set is shown below it. What is the value of each suit?

Puzzle 6
In this puzzle, Aces are low. The value of each set is shown below it. What is the value of each suit?

Solutions
These puzzles can be solved by modeling the cards algebraically and then solving by substituting in known values.

The first two puzzles require you to evaluate by substituting in the known value of the suits. The five of diamonds is represented by 5d. We know that d = 3, so our card is worth 5(3)=15. Puzzle 3 tells you the value of spades (s), and requires you to find the other values by substituting in known values and solving for unknown values. The remaining puzzles require you to find the value of one of the suits by solving a one-step equation, then find the others by repeated substitution and solving.

puzzle 1: 15, 30, 20, 30.
puzzle 2: 45, 64, 36.
puzzle 3: = 1, = 3, = 1.
puzzle 4: s = 1,  h = 5, c = 7, d = 4.
puzzle 5: s = 2,  h = 6, c = 10, d = 5.
puzzle 6: s = 11,  h = 7, c = 5, d = 2.