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DerekLin
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Angelica and Basil are playing a game with the set of ordered pairs S  18 Feb 2024, 04:51
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Angelica's final score: 7 Basil's final score: 4
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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55% (hard)

Question Stats:

64% (01:55) correct 36% (02:08) wrong based on 1644 sessions

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­Angelica and Basil are playing a game with the set of ordered pairs
\(S = {(1, 3), (2, 1), (3, 2), (4, 4)}\).
In each ordered pair, the first number is Angelica's preference number for that pair, and the second number is Basil's preference number for that pair. Angelica takes the first turn and removes an ordered pair from set S. Basil takes the second turn and removes an ordered pair from among those remaining from set S. They continue taking turns until all the ordered pairs have been removed, at which time the game is over. Each player's final score is equal to the sum of that player's preference numbers for the ordered pairs he or she has removed.

Assume that each player always selects the available ordered pair for which his or her preference number is greatest. In the table, select a value for Angelica's final score and a value for Basil's final score that are jointly consistent with this assumption and the given information. Make only two selections, one in each column.­­­­­
Angelica's final score Basil's final score
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Angelica's final score: 7 Basil's final score: 4
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Angelica and Basil are playing a game with the set of ordered pairs S  19 Mar 2024, 04:45
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­A simple question indeed… Another one of those time saver questions – only if you do not get scared of the following scenarios/terms
  1. Ordered pairs.
  2. How a game is played.

Now not all students get scared of the above. But some do and that is why mentioning this is very important so that you remove such preconceptions from your mind and recognize this question as a time-saver.

So, watch this solution and observe how easy it is to solve this question.

 ­­
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Angelica and Basil are playing a game with the set of ordered pairs S  23 Feb 2024, 19:11
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The numbers are (1,3), (2,1), (3,2) and (4,4)

A would first pick (4,4) and the score would become 4.
Next, B would be pick element containing his highest preferred number that is (1,3), so his score becomes 3.
Then A picks (3,2), making her score 4+3 or 7.
Finally B picks (2,1), making his score 3+1 or 4.

Answer: 7 and 4
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Angelica and Basil are playing a game with the set of ordered pairs S  23 Mar 2024, 22:05
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"Assume that each player always selects the available ordered pair for which his or her preference number is greatest."

Angelica takes the first turn. The largest possible pair is (4,4)

In the second turn, the largest pair to Basil is (1,3)

In the third turn, the largest pair to Angelica is (3,2)

In the final turn, the largest pair to Basil is (2,1)

So Angelica's score is 4+3=7
Basil's score is 3+1=4
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Angelica and Basil are playing a game with the set of ordered pairs S  27 Mar 2024, 17:56
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DerekLin
­Angelica and Basil are playing a game with the set of ordered pairs







\(S = {(1, 3), (2, 1), (3, 2), (4, 4)}\).
In each ordered pair, the first number is Angelica's preference number for that pair, and the second number is Basil's preference number for that pair. Angelica takes the first turn and removes an ordered pair from set S. Basil takes the second turn and removes an ordered pair from among those remaining from set S. T

Assume that each player always selects the available ordered pair for which his or her preference number is greatest. 
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Given Ordered Pairs:
Angelica's preferences are in Red and Basil's preferences are in Blue.

S = {(1, 3), (2,  1), (3, 2), (4,  4)}

Angelica's turn: She removes (4,  4). Her score is 4 right now.

Available Ordered Pairs: ­S = {(1, 3), (2,  1), (3, 2)}.

Basil's turn: She removes (1, 3). Her score is 3 right now.

Available Ordered Pairs: ­S = {(2,  1), (3, 2)}.

Angelica's turn: She removes (3,  2). Her score is 4+3 = 7 now.

Available Ordered Pairs: S = {(2,  1)}.

Basil's turn: She removes (2, 1). Her score is  3  +   1 =  4 now.
 ­
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Angelica and Basil are playing a game with the set of ordered pairs S  07 Nov 2024, 16:52
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It is easy to solve find the best answer so math just logical thinking


PAIR ARE FOR Angelica - { 1, 2, 3, 4}
PAIR ARE FOR Basil ------{ 3, 1 , 2, 4}


First turn A choose highest value - {4} that also remove { 4} for B
than B chose remaining pair for B

PAIR ARE FOR Angelica - { 1, 2, 3}
PAIR ARE FOR Basil ------{ 3, 1 , 2}

First turn B choses the best pair - {3} that rule out {1} for A

PAIR ARE FOR Angelica - { 2, 3}
PAIR ARE FOR Basil ------{ 1 , 2}

than A choses
PAIR ARE FOR Angelica - { 2, 3}
PAIR ARE FOR Basil ------{ 1 , 2}

best pair - A - { 3} that remove { 2} for B
Total A get - 4 + 3 = 7
PAIR ARE FOR Angelica - { 2,}
PAIR ARE FOR Basil ------{ 1 }

and B left with = 3 + 1 = 4
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Angelica and Basil are playing a game with the set of ordered pairs S  01 Dec 2024, 05:46
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this one is much easier than the others
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Angelica and Basil are playing a game with the set of ordered pairs S  14 Feb 2025, 13:04
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­Angelica and Basil are playing a game with the set of ordered pairs \(S = {(1, 3), (2, 1), (3, 2), (4, 4)}\).

In each ordered pair, the first number is Angelica's preference number for that pair, and the second number is Basil's preference number for that pair. Angelica takes the first turn and removes an ordered pair from set S. Basil takes the second turn and removes an ordered pair from among those remaining from set S. They continue taking turns until all the ordered pairs have been removed, at which time the game is over. Each player's final score is equal to the sum of that player's preference numbers for the ordered pairs he or she has removed.

Assume that each player always selects the available ordered pair for which his or her preference number is greatest. In the table, select a value for Angelica's final score and a value for Basil's final score that are jointly consistent with this assumption and the given information. Make only two selections, one in each column.­

Getting a question like this one correct doesn't take a lot of thinking. So, even though, in a way, it's not an easy question, a question like this one can be a little bit of a break from the intensity of the DI section.

To get a question like this one correct, we have to understand the outlined procedure, keep things straight, and execute precisely.

Key Aspects of the Procedure

From the passage:

In each ordered pair, the first number is Angelica's preference number for that pair, and the second number is Basil's preference number for that pair.

Angelica takes the first turn, and Basil takes the second turn.

Each player's final score is equal to the sum of that player's preference numbers for the ordered pairs he or she has removed.

From the question stem:

Each player always selects the available ordered pair for which his or her preference number is greatest.

Executing the Procedure

(1, 3), (2, 1), (3, 2), (4, 4)

Angelica - (1, 3), (2, 1), (3, 2), (4, 4)

Basil - (1, 3), (2, 1), (3, 2)

Angelica - (2, 1), (3, 2)

Basil - (2, 1)

Angelica's total: 4 + 3 = 7

Basil's total: 3 + 1 = 4

Correct answer: 7, 4
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Angelica and Basil are playing a game with the set of ordered pairs S  11 Jul 2025, 08:12
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Since Angelica goes first and both players play optimally:

Turn 1 (Angelica): She will take (4,4) [her highest preference = 4]

Turn 2 (Basil): From remaining {(1,3), (2,1), (3,2)}, he takes (1,3) [his highest = 3]

Turn 3 (Angelica): From remaining {(2,1), (3,2)}, she takes (3,2) [her highest = 3]

Turn 4 (Basil): Takes (2,1) [only remaining, his preference = 1]

Final scores: Angelica = 4+3 = 7, Basil = 3+1 = 4
Answer: Angelica = 7, Basil = 4

DerekLin
­Angelica and Basil are playing a game with the set of ordered pairs
\(S = {(1, 3), (2, 1), (3, 2), (4, 4)}\).
In each ordered pair, the first number is Angelica's preference number for that pair, and the second number is Basil's preference number for that pair. Angelica takes the first turn and removes an ordered pair from set S. Basil takes the second turn and removes an ordered pair from among those remaining from set S. They continue taking turns until all the ordered pairs have been removed, at which time the game is over. Each player's final score is equal to the sum of that player's preference numbers for the ordered pairs he or she has removed.

Assume that each player always selects the available ordered pair for which his or her preference number is greatest. In the table, select a value for Angelica's final score and a value for Basil's final score that are jointly consistent with this assumption and the given information. Make only two selections, one in each column.­
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