Fair Share
Dakota and Erika buy a pizza for $12 that is half pepperoni and half veggie. They cut the pizza into 8 slices.
If Dakota likes veggie three times as much as pepperoni, what is the value of a slice that is all pepperoni?
0.75
Which of the three bowls is a fair share to Ben?
Whole Bag Bowl1 Bowl 2 Bowl 3
Ben $6 $1.75 $1.75 $2.50
Ellie $7 $2 $3 $2
Tara $8 $4.25 $2 $1.75
Bowl 3
Cindy, Jamal, and Monique are dividing a piece of land using the lone-divider method. After flipping coins, Monique has been selected to be the divider, and divides the land into three pieces. The values of the three pieces of land in the eyes of the other players are shown below
Piece 1 Piece 2 Piece 3
Cindy 60% 20% 20%
Jamal 32% 39% 29%
After Cindy and Jamal have chosen their pieces, which piece will Monique be left with?
What is the value of that piece in Monique's eyes?
Piece 3
33.33%
Five players agree to divide a cake fairly using the last diminisher method. The players play in the following order: Anne first, Betty second, Cindy third, Doris fourth, and Ellen last.
In round 1, Betty and Doris are the only diminishers
In round 2, Ellen is the only diminisher
In round 3, there are no diminishers
Which player gets her fair share at the end of:
Round 1? ___________
Round 2? ___________
Round 3? ___________
Doris, Ellen, Anne
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 8
Car 11 8 10
Tractor 2 6 5
Boat 6 7 5
Who is the highest bidder for each item?
Motorcycle : Ben (11)
Car: Abby (11)
Tractor: Ben (6)
Boat: Ben (7)
Mark and Lindsey buy a pizza for $16 that is half pepperoni and half veggie. They cut the pizza into 8 slices.
If Mark likes veggie twice as much as pepperoni, what is the value of a slice that is all pepperoni?
$1.33
Whole Bag Bowl1 Bowl2. Bowl 3
Katelyn $6. $1.75 $2.50 $1.75
Makayla $4 $2.00 $1.00 $1.00
Thomas $8 $2.00 $2.00 $4.00
Which of the three bowls is a fair share to Thomas?
Bowl 3
Janai, Heaven, Dwayne, and Cheick 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
Janai 24% 21% 29% 26%
Heaven 31% 13% 22% 34%
Dwayne 14% 15% 49% 22%
Cheik 25% 25% 25% 25%
If playing honestly, what will Janai's declaration be?
Which piece will Janai receive?
Which piece will Cheick receive?
Piece 3 and Piece 4,
Piece 4
Piece 2
A 6-foot sub valued at $35 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 piece $6 $6 $6 $6
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?
Player 1, $7
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 8
Car 11 8 10
Tractor 2 6 5
Boat 6 7 5
What is Ben's total awarded ?
$24,000
Eduardo and Guadalupe buy a pizza for $10 that is half pepperoni and half veggie. They cut the pizza into 8 slices.
If Eduardo likes veggie four times as much as pepperoni, what is the value of a slice that is all veggie?
$2.00
Roberto and Delia 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 Roberto values at $1, $3, and $5 respectively. (This means Roberto values the 100 Snickers together at $1, or $0.01 for 1 Snickers)
If Delia is the divider, and in one half puts:
25 Snickers
45 Milky Ways
80 Reese's
What is the value of this half in Roberto's eyes?
And is it a fair share?
$5.60
Fair Share: YES
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):
Piece 1 Piece 2 Piece 3 Piece 4
Danny $250 $250 $250 $250
Brianna $510 $170. $150 $170
Carlos $260 $320 $180 $240
Greedy $310 $270 $290 $130
Assuming all players bid honestly, which piece will Greedy receive?
s3
Five players agree to divide a cake fairly using the last diminisher method. The players play in the following order: Anne first, Betty second, Cindy third, Doris fourth, and Ellen last.
In round 1, there are no diminishers
In round 2, Betty and Ellen are the only diminishers
In round 3, Cindy is the only diminisher
Which player gets her fair share at the end of:
Round 1? ___________
Round 2? ___________
Round 3? ___________
Anne, Ellen, Cindy
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 320 260 300 220
Vanity 200 220 120 140
The original fair share of A is worth: $ __________
• In the initial allocation, player A:
Gets ________________________ (items) and
_________________ (pays to or gets from) the state $ __________
• After all is said and done, in the final allocation, player A:
Gets ________________________ (items) and
_________________ (pays to or gets from) the state $ __________
$130
Gets the desk, pays to..., $190,
Gets the desk, pays to..., $166.25
Pierre and Allison buy a pizza for $16 that is half pepperoni and half veggie. They cut the pizza into 8 slices.
If Pierre likes veggie four times as much as pepperoni, what is the value of a slice that is all veggie?
$3.20
Emmett and Mellody 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 Emmett values at $1, $5, and $3 respectively. (This means Emmett values the 100 Snickers together at $1, or $0.01 for 1 Snickers)
If Mellody is the divider, and in one half puts:
45 Snickers
40 Milky Ways
75 Reese's
What is the value of this half in Emmett's eyes?
And is it a fair share?
$4.70
Fairshare: YES
Piece 1 Piece 2 Piece 3 Piece 4
Danny $250 $250 $250 $250
Brianna $510 $170. $150 $170
Carlos $260 $320 $180 $240
Greedy $310 $270 $290 $130
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 stando" between Brianna and Greedy. Since Danny and Carlos are not part of the stando", 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?
220 thousands of dollars
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 piece $5 $6.50 $5 $6
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?
Player 5, $6
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 320 300 200 220
Vanity 220 200 160 100
The original fair share of A is worth: $ __________
• In the initial allocation, player A:
Gets ________________________ (items) and
_________________ (pays to or gets from) the state $ __________
• After all is said and done, in the final allocation, player A:
Gets ________________________ (items) and
_________________ (pays to or gets from) the state $ __________
$135
Gets the desk and vanity, pays to..., $405,
Gets the desk and vanity, pays to..., $377.5
Carter and Rachael buy a pizza for $10 that is half pepperoni and half veggie. They cut the pizza into 8 slices.
If Carter likes veggie three times as much as pepperoni, what is the value of a slice that is all veggie?
$1.88
Ángel and Katrice 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 Ángel values at $3, $1, and $2 respectively.
If Ángel is the divider, find a possible division that is consistent with his value system.
In this division, one half contains:
Answers Vary
Prove that your half works -_-
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 $490 $150 $190 $170
Carlos $280 $330 $210 $180
Greedy $330 $310 $310 $50
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?
S3
190,000
A 6-foot sub valued at $35 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 current piece $9.00 $7.00 $8.50 $6.00
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?
P4, $7
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 300 220 320 240
Vanity 160 200 220 180
The original fair share of A is worth: $ __________
• In the initial allocation, player A:
Gets ________________________ (items) and
_________________ (pays to or gets from) the state $ __________
• After all is said and done, in the final allocation, player A:
Gets ________________________ (items) and
_________________ (pays to or gets from) the state $ __________
$115
gets no items, gets from, $115
gets no items, gets from, $135