BrainDen.com - Brain Teasers
• 0

## Question

The inhabitants of Lyra III recognize special years when their age is of the form a=p2q where 'p' and 'q' are different prime numbers. 8 is not a special year, but 12 is.

In the Lyran III inhabitants thread, we have seen when the Lyrans become master and sage. The Lyrans have also another string attached to their special year -- they got married on their special years. The marriage proposal procedure goes as follows, which is only performed among the Lyrans on their special year.

A free girl (single, separated, divorced, widowed ...) proposes to her best preference man who is on his special year. He may accept or reject the proposal based on the following conditions.

• If he is married, and prefers his current partner to the one proposing, he will reject the proposal and the woman will stay single (free) until her next special year. If the man prefers the proposing woman to his current partner, he will accept the proposal and take the new girl as his wife. His ex need to wait for her next special year to get a chance to propose to someone.
• If he is single (free), he will take the chance to propose if there is a free girl he likes better than the one proposing. In that case, he will be hooked up with the new girl, and the one proposing will remain free until her next special year. But if he likes her most, he will accept the proposal, and get married.

Now,

( i.) Will the Lyrans get married at least once in their life time or some of them may die without getting a chance to marry someone?

( ii.) Does the marriage proposal procedure favor to men or women, and in which regard?

(iii.) Is the matching stable? Let me demonstrate by example what I mean: David -- Leila and Daniel -- Lea are two couples. If David prefers Lea to his current partner Leila, and Lea prefers David to her current partner Daniel, then we say that the matching is unstable. It would have been better to match David -- Lea and Daniel -- Leila ... at least one happy family.

## 10 answers to this question

• 0
The inhabitants of Lyra III recognize special years when their age is of the form a=p2q where 'p' and 'q' are different prime numbers. 8 is not a special year, but 12 is.

In the Lyran III inhabitants thread, we have seen when the Lyrans become master and sage. The Lyrans have also another string attached to their special year -- they got married on their special years. The marriage proposal procedure goes as follows, which is only performed among the Lyrans on their special year.

A free girl (single, separated, divorced, widowed ...) proposes to her best preference man who is on his special year. He may accept or reject the proposal based on the following conditions.

• If he is married, and prefers his current partner to the one proposing, he will reject the proposal and the woman will stay single (free) until her next special year. If the man prefers the proposing woman to his current partner, he will accept the proposal and take the new girl as his wife. His ex need to wait for her next special year to get a chance to propose to someone.
• If he is single (free), he will take the chance to propose if there is a free girl he likes better than the one proposing. In that case, he will be hooked up with the new girl, and the one proposing will remain free until her next special year. But if he likes her most, he will accept the proposal, and get married.

Now,

( i.) Will the Lyrans get married at least once in their life time or some of them may die without getting a chance to marry someone?

( ii.) Does the marriage proposal procedure favor to men or women, and in which regard?

(iii.) Is the matching stable? Let me demonstrate by example what I mean: David -- Leila and Daniel -- Lea are two couples. If David prefers Lea to his current partner Leila, and Lea prefers David to her current partner Daniel, then we say that the matching is unstable. It would have been better to match David -- Lea and Daniel -- Leila ... at least one happy family.

Without getting into any proofs or math, I offer my reasoning:

( i. ) There is a chance for anyone not to get married. A man may never even get a chance to marry if nobody decides to propose to him. A woman may never get married if she is rejected every time she proposes.

( ii. ) I think it favors women, because they always have a chance at marriage. A man may never even get a proposal, and therefore never get a chance to marry.

( iii. ) I would venture a guess that the matching is unstable because Lyrans don't always have the option to choose the man or woman they want most because their special years may not match up at the right time.

##### Share on other sites
• 0

Am I reading this right that single women can only propose on her special year? It also seems to read that a female proposes to her favorite available ("special") Lyrian, not necessarily her overall favorite.

i)Suppose there are 3 Lyrians in the universe, one female and 2 male. One male will die without ever being married.

ii)Well, it favors men in the sense that they make the final decision as to who gets married. Lyrian women get to initiate proposals, but have no say on the decision (other than to try for their favorite). They also have no say if a Lyrian man wants to marry them and they are single. Basically, Lyrian women come up with the idea to get married, but are at the mercy of Lyrian men as far as the final matchup. Also, Lyrian men can propose to Lyrian women who aren't in their special year (when they reject a proposal).

iii)A stable matching cannot be guaranteed if there are Lyrians being born. David accepted a proposal from Leila because Lea wasn't born yet at the time of proposal. Lea proposed to Daniel because David was not in his special year when hers arrived.

##### Share on other sites
• 0
Am I reading this right that single women can only propose on her special year? It also seems to read that a female proposes to her favorite available ("special") Lyrian, not necessarily her overall favorite.

That is true. The man she proposes must be in his special year... so, ya not her overall favorite

##### Share on other sites
• 0

A bunch of questions ...

1. Are there an equal number of males and females?

2. Are there new babies being born, and do the new females start looking for men on their 12th birthday?

3. Can every male on a special year can be ordered in a preference ranking for each a female who is also on her special year, and vice versa? If so, are the rankings random? Would they be the same for every person? In real life it's obviously somewhere in between.

4. What is the order of the proposals? If ranking is consistent for all people, then the outcome will be different if attractive girls ask first than it would be if the selection was random.

5. Assuming a large population, a free man will almost always end up rejecting the proposal and snagging a hotter honey, but can he do so immediately after rejecting his suitor, or does he have to wait until all the ladies have done their proposing? The former seems to be closer to what you suggested, but also seems rather unfair, since the free men who receive proposals will be able to take their new wife without argument, and thus all the babes would be snatched up quickly.

Perhaps I am over-complicating the problem statement but it seems to me that all these factors would have a bearing on the solution. That might not be true, but if I'm going to modify my previous computer simulation, I need to know.

##### Share on other sites
• 0

Just some clarification ....

1. Are there an equal number of males and females?

Yes, the number of male and female Lyrans participating in the marriage proposal is equal.

2. Are there new babies being born, and do the new females start looking for men on their 12th birthday?

Well, ya there will be new faces in year marriage ceremony ... sure babies will be born.

3. Can every male on a special year can be ordered in a preference ranking for each a female who is also on her special year, and vice versa?

yes

If so, are the rankings random?

I would say random. Preference may change in the next special year. Even in the real-life, someone may rate a woman 100% but after spending some time with her the feeling towards her might be below 50% or so.

Would they be the same for every person?

It will change. A Lyran accepts his wife b/c he rate her best (of the free ones) ... but in the next special year, the hot free next-door girl may catch his eyes ...

4. What is the order of the proposals? If ranking is consistent for all people, then the outcome will be different if attractive girls ask first than it would be if the selection was random.

Random came to my mind ... but we may discuss if the order really affects the matching

5. Assuming a large population, a free man will almost always end up rejecting the proposal and snagging a hotter honey, but can he do so immediately after rejecting his suitor, or does he have to wait until all the ladies have done their proposing? The former seems to be closer to what you suggested, but also seems rather unfair, since the free men who receive proposals will be able to take their new wife without argument, and thus all the babes would be snatched up quickly.

Only women propose, and the men accept or reject the proposal. In the case of acceptance, they will end-up being partners. If he rejects the proposal, he will take a free woman he likes best as his wife (not propose) if the man was free. But if he has already a partner, by rejecting the proposal it means he will stay with his current partner.

In conclusion, I would like to see if the proposal is in favor of men or women? If it is, can someone suggest a more fairer marriage proposal approach.

##### Share on other sites
• 0

( i.) Will the Lyrans get married at least once in their life time or some of them may die without getting a chance to marry someone?

( ii.) Does the marriage proposal procedure favor to men or women, and in which regard?

(iii.) Is the matching stable? Let me demonstrate by example what I mean: David -- Leila and Daniel -- Lea are two couples. If David prefers Lea to his current partner Leila, and Lea prefers David to her current partner Daniel, then we say that the matching is unstable. It would have been better to match David -- Lea and Daniel -- Leila ... at least one happy family.

##### Share on other sites
• 0
( i.) Will the Lyrans get married at least once in their life time or some of them may die without getting a chance to marry someone?

( ii.) Does the marriage proposal procedure favor to men or women, and in which regard?

(iii.) Is the matching stable? Let me demonstrate by example what I mean: David -- Leila and Daniel -- Lea are two couples. If David prefers Lea to his current partner Leila, and Lea prefers David to her current partner Daniel, then we say that the matching is unstable. It would have been better to match David -- Lea and Daniel -- Leila ... at least one happy family.

i)Men may die without getting a chance. Women will have many chances if they are assertive on their special years, but they may never have any marriages

ii)it favors women because they can be aggressive. Men have to be passive and wait for a proposal in order to act

iii)i would say no because the probability (whatever that is =P) would be very high for perfect matches to have coinciding special days

##### Share on other sites
• 0
i)Men may die without getting a chance. Women will have many chances if they are assertive on their special years, but they may never have any marriages

ii)it favors women because they can be aggressive. Men have to be passive and wait for a proposal in order to act

iii)i would say no because the probability (whatever that is =P) would be very high for perfect matches to have coinciding special days

for iii) I meant to say the probability would be very LOW

##### Share on other sites
• 0
In conclusion, I would like to see if the proposal is in favor of men or women? If it is, can someone suggest a more fairer marriage proposal approach.

Well, if every person forms their own random ranking of all members of the opposite gender every time they are available for marriage, then it seems unlikely that any Lyrian would go his/her entire life without marital bliss, because in those 17 billion years of life there are a tremendous number of special years. However, I would still suspect it's possible, and the likelihood would probably correlate to the size of the population.

I'll write the test program in a few days. It's basically a fun little lesson in object-oriented programming.

Do you have a suggested birth rate? How about having one baby born after each 100 years of marriage? And just to avoid shocking anyone, how about saying that they can't get married until after their 18th birthday?

##### Share on other sites
• 0
Well, if every person forms their own random ranking of all members of the opposite gender every time they are available for marriage, then it seems unlikely that any Lyrian would go his/her entire life without marital bliss, because in those 17 billion years of life there are a tremendous number of special years. However, I would still suspect it's possible, and the likelihood would probably correlate to the size of the population.

I'll write the test program in a few days. It's basically a fun little lesson in object-oriented programming.

Do you have a suggested birth rate? How about having one baby born after each 100 years of marriage? And just to avoid shocking anyone, how about saying that they can't get married until after their 18th birthday?

ya, that would make it interesting. I will also do some simulation in this regard. I don't have any idea about the birth rate, but my assumption is with those billions of years to live, they may not give birth in 9 months . You may assume some value which you think is fair.

## Create an account

Register a new account