Math Quiz.....

I have a math quiz for some of you. I'm trying to figure this out, hopefully someone can help.

It's like this....

Lets say you had the zombie Virus and you didn't know it. Each month you infect 1 new person. So at the end of year 1 you've infected 12 other people. Now each of those people also infect 1 per per month. And again each of those people infect 1 new person per month.

So by the end of year one here's how it would look:

You
12 people you've infected personally... then
66 people that they had time to infect before the year is up (ie: your first person infected 11 before the end of the year. Your second infected 10 before the end of the year etc etc... adding up to 66)

So my question is for the 3rd generation of people infected, at the rate it's spreading (1 new person pre month per new member) what is the total number of people infected before the year is up???

You
12
66
???? what's the number???

here you go its basic exponential modelling as seen here

reply to post by spartacus699


Ok...I don't know if this is right or not...but what I figured is...

Starting in Jan. a person infected 1 person a month (12 people) for the year...so the first person infected in Jan. also infected 12 people for the year;

Then in Feb. 11 people infected...

March... 10
April ... 9
May... 8
June... 7
July... 6
Aug.... 5
Sept.... 4
Oct.... 3
Nov. ...2
Dec. ...1

So the total is 90 people... not including the first person infected.

This is probably wrong...but at least I tried...

I'm gotten 2 answers: 220 or 231 Not sure if either is right? But it seems close??/

a good way is to just draw it out as a diagram so you can see the increase and can check every step manually, might take up some paper but if you need to know then its worth it

So at the start of year 2 you have 66 Zombies, wouldnt you just say each of those zombies would infect another 66 each over the course of the year?

66x66= 4356 (No calc handy, so could be wrong)

This is a higher number than I thought it would be.

Month--..Infected by you—Infected by others –Total infected
.0………......…...…0...................……......0............…….........1
.1..................12............................0..........................13
.2..................12..........................12..........................37
.3..................12..........................36..........................85
.4..................12..........................84........................181
.5..................12........................180........................373
.6..................12........................372........................757
.7..................12........................756...................…1525
.8..................12......................1524...................…3061
.9..................12......................3060...................…6133
10.................12......................6132.....................12277
11.................12....................12276.....................24565
12.................12....................24564.....................49141

Still didn't get it to format the columns correctly. Just imagine orderly columns so I can go back to moppping the kitchen floor, will you?

reply to post by spartacus699


So in a year:
1 person infects 12, 12 people infect 11, 12*11 people infect 10, 12*11*10 people infect 9 and so on so the general answer for a year is
12*11*10*9*8*7*...*1 in math terms, that's a factorial
en.wikipedia.org...
12 factorial is 479001600. That's not actually a right model though, because the odds of infecting someone who doesn't have it decrease as more people get it.

My mistake. I read the problem wrong. I thought it said that the original carrier infected 12 people per month and the others infected only one per month.

Month --- Infected by you --- Infected by others --- total infected
0---------------0------------------------0-------------------1
1---------------1------------------------0-------------------2
2---------------1------------------------1-------------------4
3---------------1------------------------3-------------------8
4---------------1------------------------7------------------16
5---------------1-----------------------15------------------32
6---------------1-----------------------31------------------64
7---------------1-----------------------63-----------------128
8---------------1----------------------127-----------------256
9---------------1----------------------255-----------------512
10--------------1----------------------511---------------1024
11--------------1---------------------1023---------------2048
12--------------1---------------------2047---------------4096

reply to post by VictorVonDoom


Yeah, you're right. 2^m.

reply to post by VictorVonDoom


Impressive.

reply to post by spartacus699


what about the variable,

if each new zombie infects other people, what happens when that zombie attacks and doesnt finish the job. the beauty of chance and free will. unless ur doing an law of of avenges(I think thats a thing) in which case, the equation would be quite different. what say you?

Originally posted by VictorVonDoom
My mistake. I read the problem wrong. I thought it said that the original carrier infected 12 people per month and the others infected only one per month.

Month --- Infected by you --- Infected by others --- total infected
0---------------0------------------------0-------------------1
1---------------1------------------------0-------------------2
2---------------1------------------------1-------------------4
3---------------1------------------------3-------------------8
4---------------1------------------------7------------------16
5---------------1-----------------------15------------------32
6---------------1-----------------------31------------------64
7---------------1-----------------------63-----------------128
8---------------1----------------------127-----------------256
9---------------1----------------------255-----------------512
10--------------1----------------------511---------------1024
11--------------1---------------------1023---------------2048
12--------------1---------------------2047---------------4096

I get 220??

reply to post by spartacus699


Like I did, you're making it more complicated than it needs to be. Simply put, if every infected person infects one more person per month, then the total number of infected people will double every month.

reply to post by VictorVonDoom


The question in the OP is referring to 3rd generation zombies ONLY (those zombies who are direct descendants of 2nd generation zombies). 1st generation zombies are zombies directly infected by you. 2nd generation zombies are zombies directly infected by zombies whom you personally infected. 3rd generation zombies are zombies who were infected directly by 2nd generation zombies. The answer you provided was TOTAL number of zombies infected.

As such, 2nd generation zombies can be calculated with: Capital-sigma notation for summation in mathematics.
11 summation (11+10+9+8+7+6+5+4+3+2+1) = 2nd generation zombies = 66.

Similarly, 10 summation + 9 summation + 8 summation + 7 summation + 6 summation + 5 summation + 4 summation + 3 summation + 2 summation + 1 summation = 3rd generation zombies = 220.

Furthermore, if you continue the process for all 12 generations of zombies and add up the total, you will arrive at the total number of zombies, such as what you provided. Or simply 2^x to calculate total number of zombies, where x = numbers of months since outbreak of zombie virus.

reply to post by Pistoche


I think I see. So the OP is looking for the number of zombies created by the zombies infected by the original zombie after one year?

reply to post by VictorVonDoom


More like: Suppose you have a child every month. Each of those children will also have a child every month. How many great-grandchildren would you have after 1 year?

Edit: I think I edited my original post while you were typing up your reply. 1 more generation from what you were referring to will do the trick

reply to post by VictorVonDoom


No, Victor Von Doom you are right. The number of zombies doubles every month, because each zombie produces one other. Its 2 the m, where m is month. Clear and simple.

the terrifying thing about this thread is I have a college degree, I've taught and tutored math in two professional settings. But I just couldn't see that simple fact. I thought for some reason I can't recall that it had something to do with factorial, and there would be a quadrillion zombies. I'm freaking serious, I couldn't see it. and many of the rest of us seem to be having the same problem.

My theory is that there is some kind of government mind control beam, which makes us all mathematically retarded zombies, and they wanted to show it to us through this thread. If you think about it, it would explain a lot: Why for instance are we so willing to put up with so much (like total surveillance) to fight terrorism when terrorism kills less than lightening strikes? It doesn't add up, but we all go along with it. But like Fry in the futurama episode "The Day the Earth Stood Stoopid"
en.wikipedia.org...
You appear to be mysteriously immune to it.

Fight the stupid beam that's effecting the rest of us, VVD!

reply to post by Pistoche


Yes, yes, that makes sense. Just like the spending on the surveillance state. Just like the national debt....

NO!!!!! I must fight it. I must fight mathematical zombieism! VVD is right!

Originally posted by tridentblue

But like Fry in the futurama episode "The Day the Earth Stood Stoopid"
en.wikipedia.org...
You appear to be mysteriously immune to it.

I guess tequilla has killed my delta brain waves.