METHOD OF MARKERS PRACTICE PROBLEMS
EXAMPLE #1: Three players (A, B & C) agree to divide the 12 items below (numbered 1
- 12). Their markers have already been placed. Identify each players’ segments.
1
2
3
4
5
6
7
8
9
10
11
12
A1
ID segments
Player A
A2 C1
B1
Segment 1
C2
Segment 2
B2
Segment 3
Player B
Player C
Determine allocation of segments and leftover.
Player A:__________ Player B:____________ Player C:___________ Leftover: _________
Example #2: Three players (A, B, and C) are dividing the array of 13 items shown below
using the method of markers.
Player A:__________ Player B:____________ Player C:___________ Leftover: _________
EXAMPLE #3: Four players (A, B, C, and D) are dividing the array of 15 items shown
below using the method of markers.
Player A:_________ Player B:__________ Player C:__________ Player D:_______ __
EXAMPLE #4: Four players (A, B, C, and D) are dividing the array of 18 items shown
below using the method of markers. The players' bids are indicated in the figure.
Player A:_________ Player B:__________ Player C:__________ Player D:_______ __
EXAMPLE #5: Sheldon, Leonard, and Penny
are dividing 3 Snickers bars, 3 Nestle Crunch
bars, and 3 bags of Skittles. The following
table shows the amount of money each player
is willing to pay for each type of candy.
Snickers
Sheldon $1.50
Leonard $0.00
Penny
$1.00
Crunch
$0.50
$0.00
$1.00
Skittles
$1.00
$1.00
$1.00
Sheldon: Fair Share = _____________; Segment = _____________________________
Leonard: Fair Share = _____________; Segment = _____________________________
Penny: Fair Share = _____________; Segment = _____________________________
EXAMPLE #6: Four players (A, B, C, and D) agree to divide some candy by the method
of markers. Player A likes Reese s Pieces (R) twice as much as M&Ms (M) or peanut
M&Ms (P). Player B likes Reese s (R) , M&Ms (M) and peanut M&Ms (P) equally. Player
C likes Reese s (R) and peanut M&Ms (P) twice as much as M&Ms (M). Player D only
like peanut M&Ms (P).
Place markers below for each player to guarantee a fair share and perform the method.
M P P P R M P M M P R M R P M M M M P M R M P M
Player A: Fair Share = _____________; Segment = _____________________________
Player B: Fair Share = _____________; Segment = _____________________________
Player C: Fair Share = _____________; Segment = _____________________________
Player D: Fair Share = _____________; Segment = _____________________________
METHOD OF MARKERS PRACTICE PROBLEMS – SOLUTIONS KEY
EXAMPLE #1: Three players (A, B & C) agree to divide the 12 items below (numbered 1
- 12). Their markers have already been placed. Identify each players’ segments.
1
2
3
4
5
6
7
8
9
10
11
12
A1
ID segments
Player A
A2 C1
B1
Segment 1
1
Segment 2
2–3
B2
Segment 3
4 – 12
1–5
6 – 10
11 – 12
4–9
10 – 12
Player B
C2
Player C
1–3
Determine allocation of segments and leftovers.
1
Player A:______________
Leftover:
10 – 12 2,3
Player C:______________
4–9
Player B:_______________
Example #2: Three players (A, B, and C) are dividing the array of 13 items shown below
using the method of markers.
8 – 10
12 – 13
1–3
4–7
Player A:__________ Player B:____________ Player C:___________
Leftover: _________
EXAMPLE #3: Four players (A, B, C, and D) are dividing the array of 15 items shown
below using the method of markers.
8–9
1
4–5
12 – 15
Player A:_________ Player B:__________ Player C:__________ Player D:_______ __
Leftover: 2, 3, 6, 7, 10, 11
EXAMPLE #4: Four players (A, B, C, and D) are dividing the array of 18 items shown
below using the method of markers. The players' bids are indicated in the figure.
17 - 18 Player B:__________
1–4
11 – 15
7–9
Player A:_________
Player C:__________
Player D:_______
__
Leftover: 5 , 6, 10, 16
EXAMPLE #5: Sheldon, Leonard, and Penny
are dividing 3 Snickers bars, 3 Nestle Crunch
bars, and 3 bags of Skittles. The following
table shows the amount of money each player
is willing to pay for each type of candy.
1.50 1.50 1.50
0
0
0
1.00 1.00 1.00
Snickers
Sheldon $1.50
Leonard $0.00
Penny
$1.00
Crunch
$0.50
$0.00
$1.00
Skittles
$1.00
$1.00
$1.00
.50
.50
.50
1.00
1.00
1.00
0
0
0
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
Snickers, Snickers
9/3 = 3
Sheldon: Fair Share = _____________;
Segment = _____________________________
Leonard: Fair Share = _____________;
Segment = _____________________________
3/3 = 1
Skittles
Penny: Fair Share = _____________; Segment = _____________________________
9/3 = 3
Crunch, Crunch, Crunch
EXAMPLE #6: Four players (A, B, C, and D) agree to divide some candy by the method
of markers. Player A likes Reese s Pieces (R) twice as much as M&Ms (M) or peanut
M&Ms (P). Player B likes Reese s (R) , M&Ms (M) and peanut M&Ms (P) equally. Player
C likes Reese s (R) and peanut M&Ms (P) twice as much as M&Ms (M). Player D only
like peanut M&Ms (P).
Place markers below for each player to guarantee a fair share and perform the method.
M P P P R M P M M P R M R P M M M M P M R M P M
1 1 1 1 2 1
1 1 1 1 2 1
2 1 1
1
1
1 1 1 2
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
1 1 1
1
1
1 1 1 1
1 1 1
1 2 2 2 2
1
2 1 1 2 2 1
2 2 1
1
1
1 2 1 2
1 2 1
1 2 2 2 1
1
2 1 1 2 1 1 1 2 1
1
1
1 2 1 1
1 2 1
28/4 = 7
Player A: Fair Share = _____________; Segment = _____________________________
24/4 = 6 Segment = _____________________________
Player B: Fair Share = _____________;
Player C: Fair Share = _____________;
36/4 = 9 Segment = _____________________________
Player D: Fair Share = _____________; Segment = _____________________________
32/4 = 8