# Math Fair

1. Jeremy and Adrianna buy a pizza for \$12 that is half pepperoni and half veggie. They cut the pizza into 8 slices. If Jeremy likes veggie twice as much as pepperoni, what is the value of a slice that is all pepperoni? \$ Round to the nearest cent if necessary.

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2. Francisco, Michael, and Casey are dividing a large bag of candy. They randomly split the bag into three bowls. The values of the entire bag and each of the three bowls in the eyes of each of the players are shown here:

 Whole Bag Bowl 1 Bowl 2 Bowl 3 Francisco \$5 \$3.50 \$0.75 \$0.75 Michael \$8 \$1.75 \$1.75 \$4.50 Casey \$6 \$1.75 \$2.50 \$1.75

Which of the three bowls is a fair share to Francisco? Bowl

3. Dakota and Zoe want to split a bag of fun-sized candy, and decide to use the divider-chooser method. The bag contains 100 Snickers, 100 Milky Ways, and 100 Reese’s, which Dakota values at \$2, \$1, and \$3 respectively. (This means Dakota values the 100 Snickers together at \$2, or \$0.02 for 1 Snickers) If Zoe is the divider, and in one half puts: 20 Snickers 30 Milky Ways 60 Reese’s What is the value of this half in Dakota’s eyes? \$ Is this a fair share?

4. Roy and Ashley want to split a bag of candy, and decide to use the divider-chooser method. The bag contains 100 Snickers, 100 Milky Ways, and 100 Reese’s, which Roy values at \$5, \$2, and \$4 respectively. If Roy is the divider, find a possible division that is consistent with his value system. In this division, one half contains:  Snickers  Milky Ways  Reese’s

5. Kori, Hillary, Tatiana, and Riley are dividing a piece of land using the lone-divider method. The values of the four pieces of land in the eyes of the each player are shown below

 Piece 1 Piece 2 Piece 3 Piece 4 Kori 19% 30% 35% 16% Hillary 26% 32% 22% 20% Tatiana 24% 15% 45% 16% Riley 25% 25% 25% 25%

If playing honestly, what will Kori’s declaration be?

· Piece 1

· Piece 2

· Piece 3

· Piece 4

6. A 6-foot sub valued at \$25 is divided among five players, (P1, P2, P3, P4, P5) using the last-diminisher method. The players play in a fixed order, with P1 first, P2 second, and so on. In round 1, P1 makes the first cut and makes a claim on a C-piece. For each of the remaining players, the value of the current C-piece at the time it is their turn is given in the following table:

 P2 P3 P4 P5 Value of the current C-piece \$3.00 \$6.00 \$5.50 \$3.00

Which player gets his or her share at the end of round 1?        What is the value of the share to the player receiving it? \$

7. A 6-foot sub valued at \$25 is divided among five players, (P1, P2, P3, P4, P5) using the last-diminisher method. The players play in a fixed order, with P1 first, P2 second, and so on. In round 1, P1 makes the first cut and makes a claim on a C-piece. For each of the remaining players, the value of the current C-piece at the time it is their turn is given in the following table:

 P2 P3 P4 P5 Value of the current C-piece \$3.50 \$6.50 \$6.00 \$6.50

Which player gets his or her share at the end of round 1?        What is the value of the share to the player receiving it? \$

8. Four heirs (A, B, C, and D) must fairly divide an estate consisting of two items – a desk and a vanity – using the method of sealed bids. The players’ bids (in dollars) are:

 A B C D Desk 220 240 200 300 Vanity 180 200 140 220

The original fair share of A is worth: \$  In the initial allocation, player A:       and     the estate \$ After all is said and done, in the final allocation, player A:       and     the estate \$

9. As part of an inheritance, three children, Abby, Ben and Carla, are dividing four vehicles using Sealed Bids. Their bids (in thousands of dollars) for each item is shown below.

 Abby Ben Carla Motorcycle 9 11 6 Car 12 10 8 Tractor 5 1 2 Boat 3 4 7

In the final allocation, Abby gets which items?  (click none, one, or multiple boxes)

· Motorcycle

· Car

· Tractor

· Boat

In addition, she     to/from the estate: \$

Give your answer to the last question to the nearest dollar (careful here – the original amounts were in thousands of dollars)

10. This question illustrates how bidding dishonestly can end up hurting the cheater. Four partners are dividing a million-dollar property using the lone-divider method. Using a map, Danny divides the property into four parcels s1, s2, s3, and s4. The following table shows the value of the four parcels in the eyes of each partner (in thousands of dollars):

 s1 s2 s3 s4 Danny \$250 \$250 \$250 \$250 Brianna \$470 \$180 \$200 \$150 Carlos \$300 \$320 \$190 \$190 Greedy \$340 \$300 \$300 \$60

Assuming all players bid honestly, which piece will Greedy receive?

· s1

· s2

· s3

· s4

Assume Brianna and Carlos bid honestly, but Greedy decides to bid only for s1, figuring that doing so will get him s1. In this case there is a standoff between Brianna and Greedy. Since Danny and Carlos are not part of the standoff, they can receive their fair shares. Suppose Danny gets s3 and Carlos gets s2, and the remaining pieces are put back together and Brianna and Greedy will split them using the basic divider-chooser method. If Greedy gets selected to be the divider, what will be the value of the piece he receives?  thousand dollars