Problem 11

Consider a connected graph G whose edges have distinct costs. Denote: T₁ the minimum spanning tree of G, and T₂ the second cheapest spanning tree of G.
Question: T₁ and T₂ differ in how many edges?

Problem 10

Given sequence: $r$₁, r₂, ..., r_k such that: 0< r_i <=1 and sum( r_i ) <= n . Group r_i's into groups of zize at most 1. How many groups will you use?

So Far Away

Artist: Carol King

Problem 9

"What is the number of all trees on n points with exactly n-r endpoints? "

Frozen Yogurt Pie

Ingredients

• 3 9" baked pie shell, or graham cracker crust shell


• 32 oz. carton fruit yogurt


• 1 (12 oz.) frozen whipped non-dairy topping, thawed


• Optional: fresh or frozen fruit, cut, drained or chopped

Directions

1. Mix yogurt and thawed non-dairy topping, adding fresh fruit if desired. Pile into baked pie shells. Chill. Decorate with fresh fruit if desired, before serving. Pies may be covered with cling film and foil and frozen.

2.Thaw before serving (then decorate with fresh fruit). Each pie serves 6-8. Great dessert to have for busy days. Low calorie too. Try raspberry yogurt and fresh raspberries, etc.

Super Moist Lemon Cake

(From Ruth Manta - homemade)

Ingredients

• Batter
  
  
  
  • 1 lemon cake mix
  
  
  • 1/2 cup oil (vegetable)
  
  
  • 1 cup source cream
  
  
  • 1 Tbsp. lemon juice
  
  
• Lemon mixture
  
  
  
  • 1 cup powdered sugar
  
  
  • 1/4 cup lemon juice
  
  
• Icing
  
  
  
  • 3 Tbsp. butter (soft, NOT melted)
  
  
  • 2 1/2 cups powdered sugar
  
  
  • 3 Tbsp. lemon juice(or more)- keep adding until it gets to the right softness (like thick honey)
  
  
• Non-stick cooking spray
  

Directions

1. Mix ingredients to get batter. Using non-stick cooking spray to grease a 9x13 pan. Put batter in pan. Bake at 325^o for 40-50 minutes.

2. When cake is baked, poke with a fork. Then, drizzle lemon mixture over the top of the cake. Let cake cool at room temperature.

3. Drizzle icing on top.

Problem 8

We are given n intervals on the real lines in which the number maximum number of mutually overlapping intervals is k_1. Suppose that the intervals are partitioned into r disjoint groups where a group contains at most k_2. A legal coloring of intervals satisfies: (1) overlapping intervals are not allowed to get the same color (2) intervals belonging to the same group are not allowed to have the same color.
Question: How many color will you use to color the intervals?