An Orange Consumption Problem

  • Thread starter K Sengupta
  • Start date
In summary, four perfect logicians sat around a table that had a dish with 11 oranges in it. They agreed to ask only questions that they didn't know the answers to. Darryl knew that he ate 6 oranges, so he could determine which of the 5 possibilities are correct.
  • #1
K Sengupta
113
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Four perfect logicians sat around a table that had a dish with 11 oranges in it. The chat was intense, and they ended up eating all of the oranges. Everybody had at least one orange, and everyone knew that fact, and each logician knew the number of oranges that he ate. They didn't know how many oranges each of the other ate, though. They agreed to ask only questions that they didn't know the answers to.

Their queries are as follows:

Addison:: Did you eat more oranges that I did, Braxton?

Braxton:: I don't know. Did you, Carlos, eat more oranges than I did?

Carlos: I don't know.

Darryl : Aha!

Darryl figured out how many oranges each person ate.

Can you also deduce the number of oranges consumed by each logician?
 
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  • #2
Answer (in white)

Braxton must have had at least 2 since if he only had 1, he would know the answer to the question posed him. He must have had less than 5 or he would not be able to ask the question he asked.
Carlos knew that Braxton must have had at least 2 so he must have had at least 3, or he would know the answer to the question posed him. He must also have had less than 6 or he would have known the answer to the question.
Darryl must have had 5 because in any other case, he couldn't disambiguate between possible cases. For instance, if Darryl had 4 oranges, there are at least two possibilites:
A B C D
2 2 3 4
1 2 4 4

If Darryl had 3 oranges:
A B C D
3 2 3 3
2 2 4 3

If Darryl had 2 oranges:
A B C D
3 2 4 2
2 3 4 2

If Darryl had 1 orange:
A B C D
3 3 4 1
2 4 4 1

Since Darryl knew, Darryl must have had 5 oranges
A B C D
1 2 3 5

eom.
 
  • #3
K Sengupta said:
Can you also deduce the number of oranges consumed by each logician?

Addison ate 1, Braxton ate 2, Carlos ate 2, Darryl ate 6

Darryl knows he ate 6, so there are only 5 left to have been eaten between the other 3. Initially, Darryl knows the possibilities could be (in order of Addison, Braxton, Carlos):

1, 1, 3
1, 3, 1
3, 1, 1
1, 2, 2
2, 1, 2
2, 2, 1

When Braxton states that he doesn't know if he ate more than Addison, this proves that Braxton ate at *least* 2, because otherwise Braxton could definitively say that he did NOT eat more than Addison. Hence, Darryl knows the possibilities are:

1, 3, 1
1, 2, 2
2, 2, 1

When Carlos states that he doesn't know if he ate more than Braxton, this shows (again) that Carlos ate at *least* 2. So Darryl is left with only one possibility:

1, 2, 2


DaveE
 
  • #4
jimmysnyder said:
Answer (in white)

Since Darryl knew, Darryl must have had 5 oranges
A B C D
1 2 3 5


I think that's not quite right-- if Darryl had 5 oranges, he's left with the possible situations of:

A B C D
1 2 3 5
1 3 2 5
2 2 2 5

He can't determine which of those is correct.


DaveE
 
  • #5
davee123 said:
I think that's not quite right
Carlos knew that Braxton had at least 2 for the same reason that you do. Therefore he must have had at least 3.
eom
 
  • #6
jimmysnyder said:
Carlos knew that Braxton had at least 2 for the same reason that you do. Therefore he must have had at least 3.
eom


Ahhh, true! Good catch!


DaveE
 

1. What is an "Orange Consumption Problem"?

An Orange Consumption Problem refers to a situation where the demand for oranges exceeds the supply, leading to a shortage of oranges in the market. It can be caused by various factors such as weather conditions, diseases, and changes in consumer preferences.

2. How does an Orange Consumption Problem affect the orange industry?

An Orange Consumption Problem can have a significant impact on the orange industry. It can lead to a decrease in profits for orange growers, distributors, and retailers. It can also result in higher prices for consumers and a decrease in the variety of oranges available in the market.

3. How can an Orange Consumption Problem be solved?

An Orange Consumption Problem can be solved through various measures such as increasing the production of oranges, implementing efficient distribution systems, and finding alternative sources of oranges. Additionally, implementing sustainable farming practices and promoting the consumption of other fruits can also help alleviate the problem.

4. What are the potential consequences of not addressing an Orange Consumption Problem?

If an Orange Consumption Problem is not addressed, it can have significant consequences. It can lead to a long-term decline in the orange industry, loss of jobs for those involved in the industry, and a decrease in the availability of nutritious fruits for consumers.

5. How can individuals help in preventing an Orange Consumption Problem?

Individuals can contribute to preventing an Orange Consumption Problem by being mindful of their orange consumption and not wasting the fruit. They can also support local orange growers and purchase in-season oranges to help maintain a balance between supply and demand. Additionally, educating others about the issue and promoting sustainable farming practices can also make a difference.

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