Archive | July, 2013

14. The Zombie Abundance Problem

25 Jul
maths with zombies

…because everything’s better with zombies!

You are an army general trying to work out how many soldiers you need to send in to clear a city of zombies. To have any chance of taking the city back, past experience has told you that you need to have at least one soldier for every 10 zombies – anything less than that and you will not succeed. However, if you send in too many, you will leave your base without enough soldiers to protect it if zombies attack. This means you need to send in exactly the right number of soldiers – no more, no less. To get an estimate of the number of zombies in the city, you’ve sent out a helicopter to count the number of zombies in five randomly-selected city blocks. It has counted 523 zombies in the first one, 632 in the second, 781 in the third, 421 in the fourth and 307 in the fifth one. Given that for every one zombie seen on the streets you know there’s 4 hidden from sight in the buildings, and that there are 142 similar-sized blocks in the city, how many soldiers do you need to send in to guarantee that you’ll be able to take back the city without jeopardizing the safety of your base?

A: 2,738 soldiers

B: 15,627 soldiers

C: 37,829 soldiers

D: 65,342 soldiers

Scroll down to see the right answer…









What answer did you get?

A: With that many soldiers, there’d only be one for every 138 zombies and they’ll get massacred in seconds!

B: That’s closer to the right number, but it’s still not enough since you’d only have one solder for every 24 zombies. They’ll last longer but your troops will still lose in the end.

C: Spot on. You’ll have exactly one soldier for every 10 zombies, that will be enough to clear the city without leaving your base unprotected.

D: Since you’ll have one soldier for every six zombies, you’ll be sure to win, but because you’re sending in more than you need to, you’ll risk losing your base if zombies attack – and that would be a disaster.

How to work it out: The first thing you need to do is estimate the total number of zombies in the city. To do this, you need to account for the zombies hidden in the buildings by multiplying the counts for each city block by five (this gives 2,615, 3,160, 3,905, 2,105 and 1,535 as the estimated abundance in each block). Next, you need to work out the average number of zombies in a city block. This is done by adding up the counts in each block and dividing the total by the number of blocks sampled (in this case five). This gives an average of 2,664 per city block. You know that there are 142 similar-sized blocks in the city, so if you multiply the average number of zombies per block by this value (142) you will get the estimated abundance for the whole city. In this case, this is 378,288. Now you have the number of zombies, you can work out how many soldiers you need by dividing it by ten. This gives 37,828.8, or 37,829 if you round it up to the nearest whole number (since you can’t send in a fraction of a soldier!).

While the problems provided here are copyright of Maths With Zombies, if you are a teacher, you can use any of these problems for free in your classes – but please credit Maths With Zombies as the original source (e.g. Downloaded from MathsWithZombies.wordpress.com). You can download a PDF handout of this problem from here.

If you do use this problem in a class, please post a comment here to let me know how you used it and how it was received by your students. These problems cannot be used for any commercial purpose without express written permission.


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From the author of For Those In Peril On The Sea, a tale of post-apocalyptic survival in a world where zombie-like infected rule the land and all the last few human survivors can do is stay on their boats and try to survive. Now available in print and as a Kindle ebook. Click here or visit www.forthoseinperil.net to find out more. To download a preview of the first three chapters, click here.

To read the Foreword Clarion Review of For Those In Peril On The Sea (where it scored five stars out of five) click here.

13. The Amputation Problem

18 Jul
maths with zombies

…because everything’s better with zombies!

You look at the bite on your hand and know instantly you’ve been infected. You know the virus spreads through your body along your lymph vessels and that once it reaches your heart, it will empty into your blood system and then it will be too late to do anything about it. You know the virus travels through your lymph vessels at 2.8 inches a second and that your arm is 16 inches long. How long do you have to amputate your arm before this ‘treatment’ becomes ineffective because the virus has already reached your heart? (Note: You will need to do the maths and amputate your arm in this time, so you’ll need to work out the correct answer very quickly or you won’t have time to act).

A: 5 seconds

B: 10 seconds

C: 15 seconds

D: 20 seconds

Scroll down to see the right answer…









What answer did you get?

A: That’s right, you only have five seconds to do the maths and amputate your arm before it’s too late.

B: You really think you have that long? You’ll have turned in almost half that time.

C: Something’s gone really wrong with your maths there. Luckily (or unluckily) you won’t live long enough to work out what.

D: Boy, just how slowly do you think this disease spreads? At this rate , you’ll still be reaching for the meat cleaver by the time you turn.

How to work it out: This is a relatively simple calculation. It is just the length of your arm(16 inches) divided by the speed at which the virus spreads along your lymph vessels (2.8 inches per second). This means it will reach the end of your arm in 5.71 seconds. As you can see the maths here is easy. However, you need to make sure you do it fast and accurately. This is because you will need to arrive at the right answer quick enough to take the required action, and you won’t have time to double-check your answer. In real life, this is sometimes the case with maths, and it is the speed at which you can arrive at the right answer that’s important and not just whether you can do the calculation or not.

Note: This problem is based on how real disease, rabies, infects the human body. Rabies is probably as close as we get to a real zombie disease because it’s spread through bites and turns people into violent, crazed attackers. The virus travels along nerves at a consistent speed, meaning you can work out exactly how long it will take to reach someone’s brain once they have been bitten. This is the length of time you have to get medical treatment because once rabies reaches the brain it is pretty much 100% fatal.

While the problems provided here are copyright of Maths With Zombies, if you are a teacher, you can use any of these problems for free in your classes – but please credit Maths With Zombies as the original source (e.g. Downloaded from MathsWithZombies.wordpress.com). You can download a PDF handout of this problem from here.

If you do use this problem in a class, please post a comment here to let me know how you used it and how it was received by your students. These problems cannot be used for any commercial purpose without express written permission.

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From the author of For Those In Peril On The Sea, a tale of post-apocalyptic survival in a world where zombie-like infected rule the land and all the last few human survivors can do is stay on their boats and try to survive. Now available in print and as a Kindle ebook. Click here or visit www.forthoseinperil.net to find out more. To download a preview of the first three chapters, click here.

To read the Foreword Clarion Review of For Those In Peril On The Sea (where it scored five stars out of five) click here.

12. The Prius Vs SUV Problem

4 Jul
maths with zombies

…because everything’s better with zombies!

The dead have risen and you want to get as far away as quickly as possible. You run out your house to look for some transport. You can only find two possible cars: an SUV with its 42 gallon fuel tank two-thirds full and a Prius with 9 gallons of fuel in it. The SUV does 14 mpg (miles per gallon) while the Prius does 36 mpg. Which vehicle will allow you to get further away from the zombie outbreak?

A: I’d take the SUV, it uses more gas per mile, but with all that fuel in the tank, it’ll get you further.

B: I’d take the Prius. There’s less fuel in it but it does more miles to the gallon and that will mean I can get further away.

Scroll down to see the right answer…









What answer did you get?

A: You made the right choice. Despite the fact that it’s less fuel efficient, given the amount of fuel in its tank, you will be able to get further before you run out.

B: While it might be a good choice for the environment, the Prius is a poor choice in this case. While the Prius is more efficient, meaning it can get further per gallon of fuel, the total distance you can drive is less than the SUV.

How to work it out: First you need to work out how far you can drive in the SUV. To do this, you begin by working out how much fuel it has in its fuel tank. The tank can hold 42 gallons when it’s full. If it is currently two-thirds full, it will contain two-thirds of 42 gallons. To work out how much this is, divide 42 by 3 and then multiply the answer by 2. This tells you there’s 28 gallons of fuel in the SUV’s tank. It does 14 miles per gallon, so if you multiply the amount of fuel in its tank (28 gallons) by this number, you will know how far it can travel. In this case, it’s 392 miles. Next, you move onto the Prius. Here, you already know the amount of fuel in the tank (9 gallons), so all you need to do is multiply this number by the number of miles it can do per gallon (36). This gives you 324. So despite its better fuel efficiency, the Prius will only get you 324 miles away from the zombie outbreak, while the SUV will get you 392 miles. That’s another 68 miles the zombies need to travel to get you, and in a zombie apocalypse that could be the difference between living and dying!

Note: While the problems provided here are copyright of Maths With Zombies, if you are a teacher, you can use any of these problems for free in your classes – but please credit Maths With Zombies as the original source (e.g. Downloaded from MathsWithZombies.wordpress.com). You can download a PDF handout of this problem from here.

If you do use this problem in a class, please post a comment here to let me know how you used it and how it was received by your students. These problems cannot be used for any commercial purpose without express written permission.

*****************************************************************************

From the author of For Those In Peril On The Sea, a tale of post-apocalyptic survival in a world where zombie-like infected rule the land and all the last few human survivors can do is stay on their boats and try to survive. Now available in print and as a Kindle ebook. Click here or visit www.forthoseinperil.net to find out more. To download a preview of the first three chapters, click here.

To read the Foreword Clarion Review of For Those In Peril On The Sea (where it scored five stars out of five) click here.