Example: Alex buys a chocolatestrawberry mousse cake for $12. Alex values
chocolate 3 times as much as he values
strawberry.
(a) What is the value of the chocolate half of
the cake to Alex?
(b) What is the value of the strawberry half of
the cake to Alex?
(c ) A piece of the cake is cut as shown in (ii).
What is the value of the piece to Alex?
Example: Three players (Ana, Ben and Cara)
must divide a cake among themselves. Suppose the
cake is divided into 3 slices s1, s2 and s3. The values of
the entire cake and of each of the 3 slices in the eyes of
each of the players are shown in the following table.
(a) Indicate which of the three slices are fair shares to
Ana.
(b) Indicate which of the three slices are fair shares to
Ben.
(c) Indicate which of the three slices are fair shares to
Cara.
Whole
Cake
s1
s2
s3
Ana
$12.00
$3.00
$5.00
$4.00
Ben
$15.00
$4.00
$4.50
$6.50
Cara
13.50
$4.50
$4.50
$4.50
Example:
Antigonus
Antigonus is randomly picked to be the
divider. He cuts the empire into three
pieces: Greece/Macedonia (s1), Egypt
(s2) and Asia (s3).
s1
s2
s3
33 1/3 %
33 1/3 %
33 1/3 %
25%
55%
20%
5%
60%
35%
Rome
Ptolemy
Carthage
Salaceus
Athens
Example: Four partners (Childs, Choate,
Chou and DiPalma) want to divide a piece of
land fairly using the lone-divider method. Using
a map, DiPalma divides the land nto four
parcels (s1 ,s2 ,s3 ,s4 )and the choosers make the
following declarations:
Childs: { s2 ,s3 }
Choate: { s1 ,s3 }
Chou: { s1 ,s2 }
(a) Describe a fair division of the land.
Example: Six players want to divide cake
fairly using the lone-divider method. The divider
cuts the cake into six slices (s1 ,s2 ,s3 ,s4 , s5 ,s6 )
and the choosers make the following
declarations:
Childs: {s2 ,s3 }
Choate: {s1 ,s3 }
Chou: {s1 ,s2 }
(a) Describe a fair division of the cake.