How to divide evenly

[fairdistribution]

Hi Mathematicians,

I have a question how to evenly distribute amount of days between divorced parents so that each parent gets the same amount of overnights. Please propose a solution based on the following:
Spring break is 10 days. Each parent is to get 5 days.
however the Father requests to stay with child full consecutive 9 overnights,
The mother is willing to accept that under condition that she could use those 9 consecutive overnights with the child as well in the future.
The Mother owes the Father 2 overnights with a child that she is willing to give up so that Father can use them towards his 9 overnights.
Out of 9 overnights:
5 automatically belong to Father
2 he gets from Mom for the days she owed him from past with the child
2 he requests to get additionally from Mom so that he gets total of 9 overnight.

How many overnights should the Mother get for giving up spring break plans to be also fair to Mother and to keep an equal distribution for each parent. Please write an explanation from a mathematical point of view.

 

[conway]

Hello! it can be a slow go around here. I am a philosopher not a mathematician so I wont respond directly, for fear of misleading you. Oculus8596 is an excellent mathematician, hopefully they will respond to your question! Also Alonzo is excellent!

 

[Oculus8596]

To ensure fairness and equal distribution of overnights between the parents, I will break this situation down step by step:

1. Total Spring Break Overnights:

Spring break consists of 10 overnights. Each parent is supposed to get 5 overnights.

2. Father’s Request:

The father requests 9 consecutive overnights, which exceeds his original allocation of 5 overnights. To achieve this, the following adjustments are proposed:
5 overnights automatically belong to the father (his original share).
The mother owes the father 2 overnights from the past, which she agrees to give him now.
The father requests an additional 2 overnights from the mother to reach a total of 9 overnights.

3. Mother’s Proposal:

The mother agrees to let the father have the full 9 overnights on the condition that she can use 9 consecutive overnights with the child in the future.

4. Fair Distribution Analysis:

If the father gets 9 overnights during spring break, the mother only gets 1 overnight during this period. To maintain fairness and equal distribution overall:
The mother should receive 8 additional overnights at a later time to compensate for the imbalance created during spring break. This ensures that both parents ultimately have equal time with the child (10 overnights each: 1 during spring break + 9 later for the mother, and 9 during spring break + 1 later for the father).

5. Final Answer:

To keep the arrangement fair and balanced: The mother should receive 8 additional overnights in the future to compensate for giving up her spring break plans and allowing the father to have 9 consecutive overnights.

I hope this helps.

 

[fairdistribution]

To ensure fairness and equal distribution of overnights between the parents, I will break this situation down step by step:

1. Total Spring Break Overnights:

Spring break consists of 10 overnights. Each parent is supposed to get 5 overnights.

2. Father’s Request:

The father requests 9 consecutive overnights, which exceeds his original allocation of 5 overnights. To achieve this, the following adjustments are proposed:
5 overnights automatically belong to the father (his original share).
The mother owes the father 2 overnights from the past, which she agrees to give him now.
The father requests an additional 2 overnights from the mother to reach a total of 9 overnights.

3. Mother’s Proposal:

The mother agrees to let the father have the full 9 overnights on the condition that she can use 9 consecutive overnights with the child in the future.

4. Fair Distribution Analysis:

If the father gets 9 overnights during spring break, the mother only gets 1 overnight during this period. To maintain fairness and equal distribution overall:
The mother should receive 8 additional overnights at a later time to compensate for the imbalance created during spring break. This ensures that both parents ultimately have equal time with the child (10 overnights each: 1 during spring break + 9 later for the mother, and 9 during spring break + 1 later for the father).

5. Final Answer:

To keep the arrangement fair and balanced: The mother should receive 8 additional overnights in the future to compensate for giving up her spring break plans and allowing the father to have 9 consecutive overnights.

I hope this helps.

Thank you for your answer. I wanted to bring to your attention two approaches.
One proposed per Mother and one proposed by Father and see your opinion:
Mathematically there should be only one answer that allows us to arrive at Equality

The Mother’s approach;
Both parties have a starting point 5 and 5
Because the Mother owes 2 days from past she is wiling to give them so now the father has 7 night and the mother 3 nights for even distribution.
Now outside of that Father requests extra 2 days to get to 9 but the Mother suggests that she should also be allowed to be given 2 extra in future on the same basis as father. Fair enough. Consensus is: 9 (5+2+2) for the Father and 5 (3+2)for the mother (3 + 2)
clarification
Father: 9
5 his spring break
2 that mother owes him
2 that are additionally requested
Mother
3 from spring break
2 that are additionally requested

fathers Approach:
Each one is entitled to 5 and 5
He takes 5 plus 2 that mother owes him so that’s 7 for him automatically. Now since he asks for 2 extra that’s 9 out of 10 total days but he is willing to give those 2 extra days back.
According to him the equal distribution would
9
And 3 for mom (1 left from spring break ) plus 2 of the extra days that the father also takes and is willing to give back.

Who is mathematically right?

 

[fairdistribution]

Hello! it can be a slow go around here. I am a philosopher not a mathematician so I wont respond directly, for fear of misleading you. Oculus8596 is an excellent mathematician, hopefully they will respond to your question! Also Alonzo is excellent!

How do I contact them?

 

[Oculus8596]

Thank you for your answer. I wanted to bring to your attention two approaches.
One proposed per Mother and one proposed by Father and see your opinion:
Mathematically there should be only one answer that allows us to arrive at Equality

The Mother’s approach;
Both parties have a starting point 5 and 5
Because the Mother owes 2 days from past she is wiling to give them so now the father has 7 night and the mother 3 nights for even distribution.
Now outside of that Father requests extra 2 days to get to 9 but the Mother suggests that she should also be allowed to be given 2 extra in future on the same basis as father. Fair enough. Consensus is: 9 (5+2+2) for the Father and 5 (3+2)for the mother (3 + 2)
clarification
Father: 9
5 his spring break
2 that mother owes him
2 that are additionally requested
Mother
3 from spring break
2 that are additionally requested

fathers Approach:
Each one is entitled to 5 and 5
He takes 5 plus 2 that mother owes him so that’s 7 for him automatically. Now since he asks for 2 extra that’s 9 out of 10 total days but he is willing to give those 2 extra days back.
According to him the equal distribution would
9
And 3 for mom (1 left from spring break ) plus 2 of the extra days that the father also takes and is willing to give back.

Who is mathematically right?

I will get back to you this weekend (my days off).

 

[fairdistribution]

Thank you

 

[Oculus8596]

Thank you

The situation involves negotiating the distribution of days between the mother and father, with considerations for past owed days and requests for additional days.

Let me break down each approach and see what happens.

Mother’s Approach:

Starting point: 5 days each.
Mother owes 2 days from the past, giving the father a total of 7 days (5 + 2).

Father requests an extra 2 days, bringing his total to 9 days.
Mother suggests she should also receive 2 extra days in the future, resulting in her having 5 days (3 + 2).

Father’s Approach:

Starting point: 5 days each.
Father takes 5 days plus 2 owed by the mother, totaling 7 days. He requests 2 extra days, reaching 9 days.

He proposes to give back the 2 extra days, suggesting an equal distribution of 9 days for him and 3 days for the mother.

It is important to keep in mind that both approaches aim to address the owed days and requested extra days, but they differ in how they propose to balance the distribution.

Mother’s Approach:

She acknowledges the past debt and agrees to the father’s request for extra days while also seeking future compensation for herself. This results in a distribution of 9 days for the father and 5 days for the mother.

Father’s Approach:

He focuses on the immediate distribution, taking into account the owed days and his request, but offers to return the extra days later, leading to a temporary imbalance of 9 days for him and 3 days for the mother.

The “right” approach depends on the priorities and agreements between both father and mother. If the goal is to achieve immediate fairness, the mother’s approach seems more balanced as it considers both parties’ needs equally at the current moment. However, if the father’s offer to return the extra days later is acceptable to both parties, his approach could also be considered fair over time.
Honestly, the best solution would involve open communication and agreement on how to handle both immediate and future distributions to ensure both parties feel their needs are met in a fair and impartial manner.

I hope this helps.