General Mathematics

[raecoffey]

Ah right . I knew I was missing something, and that there had to be some equivalencies and that we would have to solve for b and s...

There are five variables to solve: B number of Vreothers
S number of sisters
Girl says the number of brothers is B = (f-1)*2 where f is the number of female children, so we also have to solve f.
Boy says the number of sisters is S = (m-1) where m is the number of male children, so we also have to solve m.
Finally, we need the number of children N = B+S. So once we get m and f we get the rest of the answers.
So you could just slog it through by manually trying values for m and f, or conceivably a spreadsheet could compute the answer.

Ok wait. Are you thing me that some males and some females identify as opposite sexes than what sex they were born into? You didn't say that. Also, that would make my 2-gendered sibling a possibility because that has definitely happened where a baby is born with born parts. Do you see now how it was unfair to leave that part out?

Also, your system isn't all the way inclusive. Sure, it's Trans inclusive, but not nonbinary.

[raecoffey]

Yay we've reached 100 responses
to our Mathematics topic!

[Tdarcos]

Ok wait. Are you thing me that some males and some females identify as opposite sexes than what sex they were born into? You didn't say that.

No, I did not say that. I said,

There are five variables to solve:
Girl says the number of brothers is B = (f-1)*2 where f is the number of female children, so we also have to solve f.
Boy says the number of sisters is S = (m-1) where m is the number of male children, so we also have to solve m.
Finally, we need the number of children N = B+S. So once we get m and f we get the rest of the answers.

Also, that would make my 2-gendered sibling a possibility because that has definitely happened where a baby is born with born parts. Do you see now how it was unfair to leave that part out?

Transgenderism or "gender identity dysphoria," is a minor issue that probably affects less than 5% of the population and is probably more like 2%. Personally, if we add up all "gender-fluid" types and non-heterosexuality: gays, lesbians, bisexuals, transgendered, hermaphroditic, neuter, and non-sexual, it's probably a total of no more than 10% of the population. It looks more than it is because they make lots of noise about it.

The vast majority of the public in the US - maybe in most countries - are probably binary heterosexuals.

So, for the purpose of this math puzzle, which was written back in the 1970s or earlier, it's an issue where a female member of a binary family complains that her family has twice as many male children related to her, i.e "brothers" as it has "sisters": female children relatives One of these brothers counters she is wrong and the number of male children relatives and female ones is the same.

[raecoffey]

Ok wait. Are you thing me that some males and some females identify as opposite sexes than what sex they were born into? You didn't say that.

No, I did not say that. I said,

There are five variables to solve:
Girl says the number of brothers is B = (f-1)*2 where f is the number of female children, so we also have to solve f.
Boy says the number of sisters is S = (m-1) where m is the number of male children, so we also have to solve m.
Finally, we need the number of children N = B+S. So once we get m and f we get the rest of the answers.

Also, that would make my 2-gendered sibling a possibility because that has definitely happened where a baby is born with born parts. Do you see now how it was unfair to leave that part out?

Transgenderism or "gender identity dysphoria," is a minor issue that probably affects less than 5% of the population and is probably more like 2%. Personally, if we add up all "gender-fluid" types and non-heterosexuality: gays, lesbians, bisexuals, transgendered, hermaphroditic, neuter, and non-sexual, it's probably a total of no more than 10% of the population. It looks more than it is because they make lots of noise about it.

The vast majority of the public in the US - maybe in most countries - are probably binary heterosexuals.

So, for the purpose of this math puzzle, which was written back in the 1970s or earlier, it's an issue where a female member of a binary family complains that her family has twice as many male children related to her, i.e "brothers" as it has "sisters": female children relatives One of these brothers counters she is wrong and the number of male children relatives and female ones is the same.

Sorry if your system isn't up with the times but I have a nonbinary 25 year old and I just won't let them be left out!

[raecoffey]

I realize now that if we solved for all of the siblings, b, s, etc... that if we also had to solve for nonbinary, it would just be irrational?

Do you have any other idea how it would look? Because while we can account for Trans if we solve for all 5 variables, we cannot have fractional children i.e solving for nonbinary.

I'm thinking imaginary numbers?

[Tdarcos]

I have beem trying four times to post an explanation on how to solve this problem, where a technician has to install a space navigation beacon on a satellite; I have been depending on something undependable. I will only look at the easier problem #7, where only one technician is needed to run the caravan.

Let me summarize the details

Problem #7
The satellite is 250 sectors away,
Each resupply ship has 70 cargo units.
Ship travels 10 sectors a day
Fuel requires 1 cargo unit for two sectors
Food requires 1 cargo unit per day per person
The Beacon uses 10 cargo units
Replacing the beacon requires one day.
A ship requires fuel to accelerate to the satellite, to brake, to accelerate home, and to brake on return.

"What is the minimum number of ships necessary to be sent out to replace the beacon and return the technician (and all resupply operators) alive and unhurt to home base?"

What we know is the trip is going to require 51 days; 25 outbound, 1 to install, 25 back.
Food required is 51 units
Fuel required for the primary ship is 500 cargo units. This means the primary ship requires 500 units of fuel, requiring 8 ships worth of fuel. But you have to get those back too so you would need the same thing. At some point you could hit the law of diminishing returns, where the additional cargo capacity of another ship is consumed as overhead. So you take another tack. Figuring out what other solution you can use.

[pinback]

[Tdarcos]

Let me get this straight from the horse's… mouth, or whichever end it is. Pinback, are you seriously trying to claim you didn't expect there would be any math in a thread titled "General Mathematics"?

[pinback]

Very seriously.

[Tdarcos]

Problem #7
The satellite is 250 sectors away,
Each resupply ship has 70 cargo units.
Ship travels 10 sectors a day
Fuel requires 1 cargo unit for two sectors
Food requires 1 cargo unit per day per person
The Beacon uses 10 cargo units
Replacing the beacon requires one day.
A ship requires fuel to accelerate to the satellite, to brake, to accelerate home, and to brake on return…
[deleted]
What we know is the trip is going to require 51 days; 25 outbound, 1 to install, 25 back.
Food required is 51 units
Fuel required for the primary ship is 500 cargo units. This means the primary ship requires 500 units of fuel, requiring 8 ships worth of fuel.

So that is what we need to get him there, but unless it is a one-way trip, we have to get him back.

What we can realize is that a cargo unit of fuel is enough to move the ship one sector. So let's try the first rule of software solutions: get it to work, first, then optimize the solution.

So, what we'll do is send him out with 71 ships (one, with food only but 7 spare units). We have 70 ships with a total of 4,900 cargo units of fuel. Each ship moved requires one cargo unit per ship per sector. We simply have to get him to the satellite with enough fuel to returrn with enough ships to carry enough fuel to return.

• Ship 1 moves all ships 1 sector. Discard it.
• Ship 2 moves all ships 1 sector. Has 1 unit of fuel left. Transfer to Ship #0. Discard ship #2.
• Repeat 6 times.

Clearly, this isn't going to work as it means we need possibly 250 ships. Let's consider another method. Staging.

[raecoffey]

Problem #7
The satellite is 250 sectors away,
Each resupply ship has 70 cargo units.
Ship travels 10 sectors a day
Fuel requires 1 cargo unit for two sectors
Food requires 1 cargo unit per day per person
The Beacon uses 10 cargo units
Replacing the beacon requires one day.
A ship requires fuel to accelerate to the satellite, to brake, to accelerate home, and to brake on return…
[deleted]
What we know is the trip is going to require 51 days; 25 outbound, 1 to install, 25 back.
Food required is 51 units
Fuel required for the primary ship is 500 cargo units. This means the primary ship requires 500 units of fuel, requiring 8 ships worth of fuel.

So that is what we need to get him there, but unless it is a one-way trip, we have to get him back.

What we can realize is that a cargo unit of fuel is enough to move the ship one sector. So let's try the first rule of software solutions: get it to work, first, then optimize the solution.

So, what we'll do is send him out with 71 ships (one, with food only but 7 spare units). We have 70 ships with a total of 4,900 cargo units of fuel. Each ship moved requires one cargo unit per ship per sector. We simply have to get him to the satellite with enough fuel to returrn with enough ships to carry enough fuel to return.

• Ship 1 moves all ships 1 sector. Discard it.
• Ship 2 moves all ships 1 sector. Has 1 unit of fuel left. Transfer to Ship #0. Discard ship #2.
• Repeat 6 times.

Clearly, this isn't going to work as it means we need possibly 250 ships. Let's consider another method. Staging.

You didn't give me time.
I'm having a rough couple of days. I was gonna take a stab at it today. No more crazy problems til after my bday and past Paddy's day and my mom's birthday 3.20. So 3.21.23, the 1st day of spring, u will be up for trying something where I have to write it out, geesh!

[Tdarcos]

You didn't give me time.
I'm having a rough couple of days. I was gonna take a stab at it today. No more crazy problems til after my bday and past Paddy's day and my mom's birthday 3.20. So 3.21.23, the 1st day of spring, u will be up for trying something where I have to write it out, geesh!

Actually, I'm trying to figure out if there is a solution. I realize I was doing it wrong. I didn't think anyone was interested. I'll wait for a while before offering a (or more than one) solutuon. I have at least two ways to try for a solution.

[raecoffey]

Ok but I'm not looking at it on my birthday weekend.

[Tdarcos]

Earlier, at this link, I spoke about Problem #7, where you have to send a technician out to a satellite, to replace a destroyed beacon. I'm going to talk about how to solve the problem, and realize that it was badly formed, in that, it can be solved, but it takes a lot of supply ships to allow the supply ship to get there.Or the program I wrote to solve it had bugs. I'm beginning to suspect the latter and it was less than I thought.

The problem is getting the fuel to come back. Getting there is easy enough. Each pair of fuel tanks provides enough fuel to move itself and a full fuel tank 35 sectors. The distance is 250 sectors, so the trip, beacon replacement, and return will take 51 days. The technician's ship carries food suppplies and the beacon, additional ships carry fuel.

I will "show my work," if you're not interested in the nitty gritty, go on to the last 2 parahraphs of this message.

Ship #2 carries 70 units of fuel, enough to move it, and #1, 35 sectors. Ship #2 is now empty.
Ships #3 and #4 can move both of them to sector 35, with #4 now empty,

Ships 5,6 move #5 to sector 35; #7,8 -> #7 to 35; #9,10-> #9 to 35;
At 35, available: #1,3,5,7,9; #3 for return.

#1,5->#1 to 70; #7,9 ->#7 to 70
#11,12-> #12 to 35; #13,14->#13 to 35; #15,16->#15 to 35.
At 70, available #1,7,12, and 15;. #12 stays as fuel for return trip.

#1,7 -> #1 at 105;
#17,18 ->#17 at 35; #19,20 ->#19 at 35; #21,22 ->#21 at 35
#23,24 -> #23 at 35; #25,26 ->#25 at 35; #27,28 ->#27 at 35;
#29,30 ->#29 at 35;#31,32 ->#31 at 35;
#17,19->#17 at 70; #21,23->#21 at 70; #25,27->#25 at 70
#29,31->#29 at 70
#17,21->#17 at 105; #25,29->#25 at 105

#1,25 -> #1,140
#33,34 ->#33 at 35; #35,36 -> #35 at 35 #37,38 ->#37 at 35;
#39,40-> #39 at 35; #41,42 ->#42 at 35; #43,44 -> #43 at 35;
#41,42 ->#42 at 35; #43,44 -> #43 at 35; #45,46->#45 at 35;
#47,48-> #47 at 35
#33,35 -> #33 at 70; #37,39->#37 at 70; #42,43->#42 at 70
#45,47->#45 at 70
#33,37->#33 at 105; #42,45 ->#42 at 105
At 105,available: 17,33,42, Leave #17 for return

#33,42 -> #33 at 140
#1,33 -> #1 at 175

#49,50 -> #49 at 35; #51,52->#51 at 35; #49,51->#49 at 70
#53,54 -> #53 at 35; #55,56->#55 at 35; #53,55->#53 at 70
#57,58 -> #57 at 35; #59,60->#59 at 35; #57,59->#57 at 70
#61,62 -> #61 at 35; #63,64->#63 at 35; #61,63->#61 at 70
#65,66 -> #65 at 35; #67,68->#67 at 35; #65,67->#65 at 70
#69,70 -> #69 at 35; #71,72->#71 at 35; #69,71->#69 at 70
#73,74 -> #73 at 35; #75,76->#75 at 35; #73,75->#73 at 70
#75,76->#75 at 35; #77,78 -> #77 at 35;#75,77->#75 at 70
#79,89->#79 at 35; #81,82 ->#81 at 35; #79,81->#79 at 70
#83,84 -> #83 at 35; #85,86->#85 at 35; #83,85->#83 at 70
#87,88-> #87 at 35; #89,90->#89 at 35; #87,89-> #87 at 70
#91,92->#91 at 35; #93,94->#93 at 35; #91,93->#91 at 70
#95,96->#95 at 35; #97,98->#97 at 35; #95,97->#95 at 70
#99,100->#99 at 35; #101,102->#101 at 35; #99,101->#99 at 70
#49,53->#49 at 105; #57,61->#59 at 105;#49,59->#49 at 140
#57,61->#57 at 105; #65,69->#65 at 105;#57,65->#57 at 140
#73,75->#73 at 105; #79,83->#79 at 105;#73,83->#73 at 140
#87,91->#87 at 105; #95,99->#95 at 105;#87,99->#87 at 140
#49,57->#49 at 175; #73,87->#73 at 175

At 175: #1,#49,#73; Leave #49 for return
#1,73->#1 at 210


This was so complicated, I had saved this article and came back to it. At ffirst I thought I made a mistake requiring additional corrections. This is the sort of thing computers were made to solve.

So I've decided to write a new program to do the calculations. But, anyway, this example should show what is involved to do them.

[pinback]

#69,70 -> #69 at 35; #71,72->#71 at 35; #69,71->#69 at 70
#73,74 -> #73 at 35; #75,76->#75 at 35; #73,75->#73 at 70

Ya sure about that?

[RealNC]

What is the minimum number of ships necessary to be sent out to replace the beacon and return the technician (and all resupply operators) alive and unhurt to home base?

60.

(ChatGPT)

[Tdarcos]

#69,70 -> #69 at 35; #71,72->#71 at 35; #69,71->#69 at 70
#73,74 -> #73 at 35; #75,76->#75 at 35; #73,75->#73 at 70

Ya sure about that?

No. Rereading my partial solution, I don't show how #12 and #15 get from #35 to #70. It (tentatively) looks like I needed two more ships to move one of these; the other can be moved by the one already there.

[Tdarcos]

What is the minimum number of ships necessary to be sent out to replace the beacon and return the technician (and all resupply operators) alive and unhurt to home base?

60.

(ChatGPT)

I don't think that is right, considering what I did. This us why doing "show your work" is absolutely critical to show that the solution given is or is not correct.

Exactly what question did you ask ChatGPT? I have a suspicion you did not give all variables.

[pinback]

[Mama Blue]

See I love beautiful mathematics, like congruent modular forms, or fractals, or ordinary differential equations. Equations where you have to find the shortcut to substitute variables and make things look prettier. Can you find a question like that?