Five players are dividing a cake among themselves using the lone-divider method. After the divider D cuts the cake into five slices ( s 1 , s 2 , s 3 , s 4 , s 5 ) the choosers C 1 , C 2 , C 3 , and C 4 submit their bids for these shares. a. Suppose that the choosers’ bid lists are C 1 : { s 2 , s 3 } ; C 2 : { s 2 , s 4 } ; C 3 : { s 1 , s 2 } ; C 4 : { s 1 , s 3 , s 4 } Describe three different fair divisions of the land. Explain why that’s it—why there are no others. b. Suppose that the choosers bid lists are C 1 : { s 1 , s 4 } ; C 2 : { s 2 , s 4 } ; C 3 : { s 2 , s 4 , s 5 } ; C 4 : { s 2 } Find a fair division of the cake. Explain why that’s it—there are no others.
Five players are dividing a cake among themselves using the lone-divider method. After the divider D cuts the cake into five slices ( s 1 , s 2 , s 3 , s 4 , s 5 ) the choosers C 1 , C 2 , C 3 , and C 4 submit their bids for these shares. a. Suppose that the choosers’ bid lists are C 1 : { s 2 , s 3 } ; C 2 : { s 2 , s 4 } ; C 3 : { s 1 , s 2 } ; C 4 : { s 1 , s 3 , s 4 } Describe three different fair divisions of the land. Explain why that’s it—why there are no others. b. Suppose that the choosers bid lists are C 1 : { s 1 , s 4 } ; C 2 : { s 2 , s 4 } ; C 3 : { s 2 , s 4 , s 5 } ; C 4 : { s 2 } Find a fair division of the cake. Explain why that’s it—there are no others.
Solution Summary: The author explains the three fair divisions of the land using the lone-divider method.
Five players are dividing a cake among themselves using the lone-divider method. After the divider
D
cuts the cake into five slices
(
s
1
,
s
2
,
s
3
,
s
4
,
s
5
)
the choosers
C
1
,
C
2
,
C
3
, and
C
4
submit their bids for these shares.
a. Suppose that the choosers’ bid lists are
C
1
:
{
s
2
,
s
3
}
;
C
2
:
{
s
2
,
s
4
}
;
C
3
:
{
s
1
,
s
2
}
;
C
4
:
{
s
1
,
s
3
,
s
4
}
Describe three different fair divisions of the land. Explain why that’s it—why there are no others.
b. Suppose that the choosers bid lists are
C
1
:
{
s
1
,
s
4
}
;
C
2
:
{
s
2
,
s
4
}
;
C
3
:
{
s
2
,
s
4
,
s
5
}
;
C
4
:
{
s
2
}
Find a fair division of the cake. Explain why that’s it—there are no others.
i) Consider the set S = {−6, −3, 0, 3, 6}. Draw a graph G whose set of verti-
ces be S and such that for i, j ∈ S, ij ∈ E(G) if ij are related to a rule that t'u
you choose to apply to i and j.
(ii) A graph G of order 12 has as a set of vertices c1, c2, . . . , c12 for the do-
ce configurations of figure 1. A movement on said board corresponds to moving a
coin to an unoccupied square using the following two rules:
1. the gold coin can move only horizontally or diagonally,
2. the silver coin can move only vertically or diagonally.
Two vertices ci, cj, i̸ = j are adjacent if it is possible to move ci to cj in a single movement.
a) What vertices are adjacent to c1 in G?
b) Draw the subgraph induced by {c2, c6, c9, c11}
2. Find the exact value of 12 + 12+12+√√12+ √12+
12
he following contingency table details the sex and age distribution of the patients currently registered at a family physician's medical practice. If the doctor sees 17 patients per day, use the binomial formula and the information contained in the table to answer the question:
SEX
AGE
Under 20
20-39
40-59
60-79
80 or over
TOTAL
Male
5.6%
12.8%
18.4%
14.4%
3.6%
54.8%
Female
2.8%
9.6%
13.2%
10.4%
9.2%
45.2%
TOTAL
8.4%
22.4%
31.6%
24.8%
12.8%
100.0%
if the doctor sees 6 male patients in a day, what is the probability that at most half of them are aged under 39?
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