General Mathematics

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Flack
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Re: Problem #7

Post by Flack »

Tdarcos wrote: Mon Mar 20, 2023 5:57 am 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.
Fuck, I had it except I switched 67 and 65.
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Tdarcos
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Re: Problem #7

Post by Tdarcos »

I found way to do it. What is it he has to dfo? Cover a distance and return. So he needs enough fuel to get there and come back. So, figure what he needs and what it will take to get there. The trip is made in 35 sector segments.
0. 0
1. 35
2. 70
3. 105
4. 140
5. 175
6. 210
7. 245
8. 250.

To get to segment 8, he needs to have fuel to return to 7, so he needs 1 ship and 1 tank, 2 tanks in order to have fuel to return (one for fuel, one to lift the fuel) . So he needs his ship and 3 fuel tanks.
8. 4
To get to segment 7, he needs those 4, 1 to return to segment 6, and 5 tanks to lift them
7. 10
To get to segment 6, he needs those 10, 1 to return to segment 5, 11 to lift them
6. 22
To 5: Those 22, 1 return to 4, 23 to lift.
5. 46
To 4: Those 46, 1 to return to 3, 47 to lift.
4. 88
To 3: those 88, 1 to return,, 89 to lift
3. 177
To 2: Those 177, 1 to return, 178 to lift
2. 355
To 1: Those 355, 1 to return, 356 to lift
1. 712
At Base: One ship and 713 tanks lifted by 714 tanks. 1,428 vehicles; 1 ship and 1,427 fuel tanks

Now test the calculation.
Base-0 Sectors: One ship and 713 tanks lifted by 714 tanks; on reaching segment 1,one kept for return trip
Segment 1-35 Sectors: 712 vehicles lift off: One ship, 356 fuel tanks lifted by 357 tanks to segment 2, 35 sectors. 357 tanks discarded as empty. One stays for return.
2- 70: 354 remain. One ship and 177 tanks are lifted by 178 tanks to segment 3; 35 sectors, 178 tanks discarded as empty, one stays for return.
3-105: 176 remain. One ship and 88 tanks are lifted to segment 4 by 89 tanks, 1 stays
4-140: 88 remain. One ship and 46 tanks lifted by 87 tanks, 1 stays
5-175: 46 remain. One ship and 22 tanks lifted by 43 tanks, 1 stays
6-210: 22 remain. One ship and 9 tanks lifted by 11 tanks, 1 stays
7-245: 10 remain: One ship and 4 tanks lifted by 5 tanks, 1 stays
8=250: 4 remain. One ship and 1 tank for return lifted by 2 tanks.
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Ice Cream Jonsey
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Re: Problem #7

Post by Ice Cream Jonsey »

Tdarcos wrote: Wed Mar 22, 2023 6:01 pm I found way to do it. What is it he has to dfo? Cover a distance and return. So he needs enough fuel to get there and come back. So, figure what he needs and what it will take to get there. The trip is made in 35 sector segments.
0. 0
1. 35
2. 70
3. 105
4. 140
5. 175
6. 210
7. 245
8. 250.

To get to segment 8, he needs to have fuel to return to 7, so he needs 1 ship and 1 tank, 2 tanks in order to have fuel to return (one for fuel, one to lift the fuel) . So he needs his ship and 3 fuel tanks.
8. 4
To get to segment 7, he needs those 4, 1 to return to segment 6, and 5 tanks to lift them
7. 10
To get to segment 6, he needs those 10, 1 to return to segment 5, 11 to lift them
6. 22
To 5: Those 22, 1 return to 4, 23 to lift.
5. 46
To 4: Those 46, 1 to return to 3, 47 to lift.
4. 88
To 3: those 88, 1 to return,, 89 to lift
3. 177
To 2: Those 177, 1 to return, 178 to lift
2. 355
To 1: Those 355, 1 to return, 356 to lift
1. 712
At Base: One ship and 713 tanks lifted by 714 tanks. 1,428 vehicles; 1 ship and 1,427 fuel tanks

Now test the calculation.
Base-0 Sectors: One ship and 713 tanks lifted by 714 tanks; on reaching segment 1,one kept for return trip
Segment 1-35 Sectors: 712 vehicles lift off: One ship, 356 fuel tanks lifted by 357 tanks to segment 2, 35 sectors. 357 tanks discarded as empty. One stays for return.
2- 70: 354 remain. One ship and 177 tanks are lifted by 178 tanks to segment 3; 35 sectors, 178 tanks discarded as empty, one stays for return.
3-105: 176 remain. One ship and 88 tanks are lifted to segment 4 by 89 tanks, 1 stays
4-140: 88 remain. One ship and 46 tanks lifted by 87 tanks, 1 stays
5-175: 46 remain. One ship and 22 tanks lifted by 43 tanks, 1 stays
6-210: 22 remain. One ship and 9 tanks lifted by 11 tanks, 1 stays
7-245: 10 remain: One ship and 4 tanks lifted by 5 tanks, 1 stays
8=250: 4 remain. One ship and 1 tank for return lifted by 2 tanks.
Wrong
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Jizaboz
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Re: General Mathematics

Post by Jizaboz »

Ice Cream Jonsey wrote: Wed Mar 22, 2023 7:56 pm Wrong
ROFL got dam mang that one hurt lol
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RealNC
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Re: General Mathematics

Post by RealNC »

Let's see if Bing's AI (GPT4) fares any better:

Image

"Show me some recipes" is clearly the appropriate answer here.

Image

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Tdarcos
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Re: General Mathematics

Post by Tdarcos »

This is why I originally said AI was not correct and still isn't. I could not figure out how to solve the problem until I realized the answer could be found by starting at the end and working backward. As I said earlier, this is one of those cases where "showing your work" is critical, because unless you have a provable solution, you don't know if the answer is correct.

I did write a program to try to solve this, by brute force, i.e. from base, add fuel tanks until you get there. I need to see what it came up with. I originally wrote it figuring 500 would be enough. How wrong I was! It never really finds the solution, because it's clearly not solving it correctly.
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Tdarcos
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Re: Problem #9 - Depot Refuel

Post by Tdarcos »

Tdarcos wrote: Sun Feb 12, 2023 8:48 am deliver fuel to a depot that is empty, 1000 miles away,
1000 gallons of gas and 1000 gallons of gasoline to the depot
your trucks have a 200 mile range
gasoline delivery trucks run on diesel, diesel delivery vehicle runs on gasoline
Gasoline delivery trucks have a 20 gallon diesel fuel tank
diesel delivery trucks have a 20 gallon gasoline fuel tank
Both have 200 gallon delivery tanks
All trucks get 10MPG
So, first we have to get 1 diesel and 1 gasoline truck to the depot. Each requires 200 gallons of fuel for the round trip.
We will need 4 trucks. Diesel Delivery truck #1 and Gasoline Delivery truck #1 are emptied at arrival.
Diesel Delivery truck #2 provides 200 gallons each for gasoline delivery trucks #1 and #2.
Gasoline Delivery truck #2 provides 200 gallons each for diesel delivery trucks #1 and #2.
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Mama Blue
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Re: General Mathematics

Post by Mama Blue »

This is why i wasn't interested in this problem...

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Tdarcos
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Problem #10

Post by Tdarcos »

Mama Blue wrote: Sun Mar 26, 2023 6:56 pm This is why i wasn't interested in this problem...
I did these off the top of my head. By pure accident #7 is a relatively difficult problem and #9 is trivially easy. I'm trying to think of another one.

A man goes into a store. He looks over the stock and find i he buys 1, it will cost 89c, if he buys 12, it will cost $1.78, and to purchase 123, it will cost $2.67. Plus tax. What is he buying?
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Mama Blue
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Re: Problem #10

Post by Mama Blue »

Tdarcos wrote: Mon Mar 27, 2023 10:04 am

A man goes into a store. He looks over the stock and find i he buys 1, it will cost 89c, if he buys 12, it will cost $1.78, and to purchase 123, it will cost $2.67. Plus tax. Ts. is he buying?
This is not a math problem. He's buying multiples of something that costs 89 cents.

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Re: General Mathematics

Post by pinback »

Let's get some goddamn math in here, Paul. Enough with your little word games.

He's buying numbers for mailboxes or some stupid shit like that.
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Re: General Mathematics

Post by Ice Cream Jonsey »

All it took for that puzzle, then, is to just completely ignore HOW ENGLISH WORKS, by calling it "123" instead of "1, 2 and 3."

BAD PUZZLE!!!!!!!!!
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Re: General Mathematics

Post by AArdvark »

I remember that one from sixth grade. At the time it was clever.

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Re: General Mathematics

Post by Ice Cream Jonsey »

Okay, I stand corrected.

Tdarcos, now that I think about it, I agree, that's a fine puzzle.
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Mama Blue
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Re: General Mathematics

Post by Mama Blue »

Do you guys know any linear algebra, or how to work with matrices?

I have some good screenshots I can post here. How do I do that?

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Tdarcos
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Re: General Mathematics

Post by Tdarcos »

Mama Blue wrote: Tue Mar 28, 2023 12:53 pm Do you guys know any linear algebra, or how to work with matrices?

I have some good screenshots I can post here. How do I do that?
You either need your own hosting, can get someone else to host it on theirs, or get an account on a photo sharing service and host them there.

Https://ctrlq.org claims to offer free image hosting without needing an account, but it looks to me like it has problems. This article https://www.guru99.com/free-photo-hosting.html lists 15 sites that offer free image hosting.
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Mama Blue
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Re: General Mathematics

Post by Mama Blue »

Tdarcos wrote: Tue Mar 28, 2023 6:43 pm
Mama Blue wrote: Tue Mar 28, 2023 12:53 pm Do you guys know any linear algebra, or how to work with matrices?

I have some good screenshots I can post here. How do I do that?
You either need your own hosting, can get someone else to host it on theirs, or get an account on a photo sharing service and host them there.

Https://ctrlq.org claims to offer free image hosting without needing an account, but it looks to me like it has problems. This article https://www.guru99.com/free-photo-hosting.html lists 15 sites that offer free image hosting.
I'm sorry, I did not ask the correct question. Where can I host multiple images, for free, at once?

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Re: General Mathematics

Post by pinback »

imgur
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Mama Blue
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Re: General Mathematics

Post by Mama Blue »

Well ingur gave me this link, if everyone could visit it. It is the very basics of linear algebra and the mathematics of matrices for anyone who doesn't know it. I figure with all of the computer/ video game programming, that an introduction to matrices might be a valuable assett.

https://imgur.com/gallery/TLLOYZ1

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Re: General Mathematics

Post by Tdarcos »

Tdarcos wrote: Sat Feb 11, 2023 11:37 am Problem #2 (And try doing this without using the internet).

Two kids from a family are talking.

The Girl: This is unfair! I have twice as many brothers as sisters!
The Boy: That's wrong, sis. We have the same number of brothers and sisters.

1. Both statements are correct.
2. You have enough information to tell us the number of children in that family and their sexes.


I told this to one of my teachers, he solved the problem in a few seconds, and he was my English teacher. This explained why once, in math class, our math teacher told us our most important class was English.
I'll make an exception here and show how ChatGPT solved it.
>A girl says it's unfair because she has twice as many brothers as sisters. He says that they have the same number of brothers and sisters. Both are right. How many children are in this family of each sex?

Let's assume there are N total children in the family, with B brothers and S sisters.

According to the girl, she has twice as many brothers as sisters. This can be represented as:

B = 2S

According to the boy, they have the same number of brothers and sisters. This can be represented as:

B = S

We can solve these two equations simultaneously to find the values of B and S.

Substituting B = S into the first equation gives:

S = 2S/2

Simplifying:

S = S

So the girl has correctly identified that she has twice as many brothers as sisters, which means that there are 2S brothers and S sisters in the family.

Substituting B = S into the second equation gives:

B = B/2

Simplifying:

B = 0

This is a contradiction, as it implies that there are no children in the family. Therefore, the boy's statement cannot be correct.

Thus, the only solution consistent with the girl's statement is that there are twice as many brothers as sisters. Therefore, we have:

B = 2S

And the total number of children is:

N = B + S = 2S + S = 3S

Since N, B, and S are all integers, the only possible solution is if S = 2 and B = 4, which satisfies both statements:

The girl has twice as many brothers as sisters (4 brothers, 2 sisters).
The boy and girl have the same number of brothers and sisters (4 brothers, 2 sisters).


- - - -
And he got it wrong because he didn't count her. The correct answer is 4 boys and 3 girls.
The girl sees two sisters and four brothers; he sees three of each. As they said, sometimes it is wrong.


>Your answer is not correct. You missed counting the girl. B=4 and S=2 do not work. She would see three brothers and 1 sister, he would see the same. The only correct answer is 4 boys and 3 girls.
The girl sees two sisters and four brothers; he sees three of each.

I apologize for my mistake in the previous answer. You are correct that I overlooked the girl's presence in the family, and as a result, my solution was incorrect. Thank you for pointing that out and providing the correct answer.

Indeed, if we include the girl in the family, the correct solution is that there are 4 boys and 3 girls. The girl sees two sisters and four brothers, which means that there are three girls in total (including herself) and four boys. The boy sees three of each, which confirms that there are 4 boys and 3 girls in the family.
Alan Francis wrote a book containing everything men understand about women. It consisted of 100 blank pages.

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