Discrete Math Fair Division

Three players (Ady, Brenden, and Cara) are sharing a pie. Suppose that the pie is divided into three slices (S1 ,S2 , and S3 ). The following table gives the value of each slice in the eyes of each of the players.

Which of the three slices are fair shares to Ady?

• S1

• S3

• S1, S2

• S1, S3

Tags

CCSS.3.NF.A.1

CCSS.3.NF.A.2B

Four heirs must divide an estate consisting of a house and a cabin. Use the table to determine how much is a fair share to Player A?

• $240,000

• $80,000

• $120,000

• $60,000

Four heirs must divide an estate consisting of a house and a cabin. In the initial allocation, what did player B receive?

• Player B gets $62,000 from the estate

• Player B gets the house and cabin, and pays $186,000 to the estate

• Player B gets the house and pays the estate $274,000

• Player B gets the house and pays the estate $150,000

Four players divide the 12 items using the method of markers. Who will receive Item #5?

• C

• A

• D

• leftover

• B

Tags

CCSS.3.OA.A.2

Four players divide the 12 items using the method of markers. Who will receive Item #8?

• A

• B

• C

• D

• leftover

Four players divide the 12 items using the method of markers. Who will receive Item #11?

• A

• B

• C

• D

• leftover

A cake is divided among seven players (P₁, P₂, P₃, P₄, P₅, P₆ and P₇) using the last-diminisher method. In round 1, after P1 makes the first cut, all the other players pass. In round 2, after the first claim is made, P₃, P₆ and P₇ are the only diminishers. Who makes the first claim in round 3 ?

• Player 2
• Player 3
• Player 1
• Player 7

Four friends have decided to divide up a multi-flavored cake which was jointly purchased for $24. The cake is divided into four pieces. The following table gives the dollar value of each of the slices according to each of the four friends.
Who was the divider?

• Justin
• Tatiana
• Mollie
• Charlie

Tags

CCSS.4.NF.A.1

CCSS.5.NF.B.5B

Four players are dividing land using the lone divider method.  If the choosers declarations are Chooser 1: {s₂, s₃},  Chooser 2: {s₂, s₄} and Chooser 3: {s₁, s₃}, which of the following is NOT a fair division of the cake?

• Chooser 1 gets s₂;
  Chooser 2 gets s₄;
  Chooser 3 gets s₃;
  Divider gets s₁.
• Chooser 1 gets s₂;
  Chooser 2 gets s₄;
  Chooser 3 gets s₁;
  Divider gets s₃.
• Chooser 1 gets s₃;
  Chooser 2 gets s₂;
  Chooser 3 gets s₄;
  Divider gets s₁.
• Chooser 1 gets s₃;
  Chooser 2 gets s₄;
  Chooser 3 gets s₁;
  Divider gets s₂.

Four friends have decided to divide up a multi-flavored cake which was jointly purchased for $24. The cake is divided into four pieces. The following table gives the dollar value of each of the slices according to each of the four friends.  Which piece of the cake will Justin get?

• S1
• S2
• S3
• S4