Archive | May, 2013

7. The Rapid Fire Problem

30 May
maths with zombies

…because everything’s better with zombies!

You are armed with a machine gun that can fire 131 bullets per minute; that’s a lot of bullets but it’s not very accurate and you only hit 30% of the zombies you fire at. Suddenly a swarm of 400 zombies appears over a nearby hill and they’re moving quickly (they’re these pesky new fast zombies!). You estimate they’ll at the door to your compound in 10 minutes and if that happens you’ll be over-run. Is there enough time to kill all the zombies with your machine gun before they get there? If there is your best option is to stand and fight. If not, you should run now. You’ll have to leave all your supplies and gear behind and start afresh somewhere new; it won’t be easy, but at least you’ll be alive!

A: I’ll get them all just in time, my best option is to stay and fight.

B:There’s not enough time to kill all the zombies before they get here. I need to get out now.

Scroll down to see the right answer…









What answer did you get?

A: Uh-oh, something when wrong with your calculations. You should have turned and run; instead you’ll end up as zombie chow.

B: Well done, you got the maths right and you’ll live to fight another day. You must have worked out that you’ll only kill 393 of the 400 zombies by the time they get to you.

How to work it out: The machine gun can fire 131 bullets a minute. If you multiply this by the length of time you have to kill all the zombies (10 minutes), you’ll find that you can fire 1,310 bullets in that length of time. That would be more than enough bullets if it wasn’t for the lack of accuracy. The gun is only 30% accurate. When expressed as a probability, this is 0.3. This means that for every 10 shots fired, you’ll only kill three zombies. If you multiply the number of bullets you can fire in 10 minutes (1,310) by probability of each bullet killing a zombie (0.3), you’ll find that despite firing over 1,000 bullets, you’ll only kill 393 zombies. This means there will be 7 left to over-run your defences.

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.

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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.

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6. The Injured Friend Problem

23 May
maths with zombies

…because everything’s better with zombies!

You can see the zombies coming towards you. You estimate that they’re moving at about 4 miles an hour. Normally you’d be able to out run them no problem but today your carrying your best friend who’s just broken his leg and can’t walk. This means you can only move at 1 miles an hour (he might be your friend but he’s heavy!). You can see the door to your safe house at the end of the street. It’s 83 yards away. You look back over your shoulder, the zombies are 250 yards behind you. You have two options: You can carry on with your friend but he’ll slow you down or you can abandon him so you can move faster. Will you still make it to your safe house before the zombies get there? (hint: There’s 1,760 yards in a mile).

A: Yes, so the best thing to do is keep carrying my friend.

B: No, so the only way I’ll survive is if I abandon my friend so I can run faster.

Scroll down to see the right answer…









What answer did you get?

A: You got it right. You’ll arrive at the safe house just half a second before the zombies. Just as well you didn’t get it wrong and accidentally go for B.

B: Oh no! You got your maths wrong and now your friends being eaten alive by zombies when you could have made it even without abandoning him. You did get the maths wrong didn’t you? You didn’t just abandon him, did you? Humm, I’m not too sure I trust you any more …

How to work it out: First, the zombies to reach the safe house: They can travel at 4 miles an hour, that’s 7,040 yards (4 * 1760 or the number of yards in a mile). This means they will cover the 333 yards to the safe house (the 83 yards between you and the safe house plus the 200 yards between you and the zombies) in 0.0473 hours. This is worked out by dividing the distance they need to cover (283 yards) by the distance they can travel in an hour (7,040 yards). 0.0473 hours is the equivalent of 2 minutes and 50.3 seconds. You’ve only got 83 yards to cover but you’re moving much slower. You can only cover one mile or 1,760 yards in an hour. You will take 0.0472 hours (83/1,760) to reach the safe house. That’s 2 minutes and 49.8 second meaning you’ll reach safety with just a hair over half a second. If you’d been just one more yard further from the safe house, they’d have got you.

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.

5. The Hungry Zombies Problem

16 May
maths with zombies

…because everything’s better with zombies!

There’s five million people in your city and 25 graveyards. Each graveyard has 5,000 graves in it and when the zombie apocalypse comes the dead in all these graves will rise up and attack the living. How many people will each zombie have to consume before there’s no one left?

A: 10.

B: 40.

C: 100.

D: 400.

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What answer did you get?

A: That would barely make a dent in the human population of the city. There’d still be 3.75 million people left.

B: You’re right, but it’s not a lot that each zombie needs to eat to consume a whole city, is it?

C: That’s a lot of people for each zombie to eat. At that rate, they’d be able to devour two and a half cities.

D: If each zombie ate that many, they’d be able to consume ten cities worth of people, not just one!

How to work it out: First, you need to work out how many zombies there will be. This is done by multiplying the number of graves in each graveyard (5,000) by the number of graveyards in the city (25). This gives tells you that there’s 125,000 graves, and that means there will be 125,000 zombies when the dead start to rise. The average number of people each zombie needs to devour is then calculated by dividing the population size of the city (5,000,000) by the number of zombies (125,000). When you do this, you get 40. This means each zombie will have to consume 40 people before the entire city is devoured.

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.

4. The Viral Spread Problem

9 May
maths with zombies

…because everything’s better with zombies!

There’s a virus turning people into zombies who attack the living and never die. No one knows where it came from but the first person (known as ‘patient zero’ by those who study how diseases spread) was an archaeologist who’d just discovered an ancient tomb so it might have come from there. The virus is spread when infected people bite someone who’s uninfected. If each zombie bites an average of three uninfected people each day, how long will it take before the entire human population of the planet (which for this problem will be taken as 7 billion people) are turned into shambling undead flesh-munchers?

A: 167 days (almost 6 months).

B: 53 days (just under 8 weeks).

C: 17 days (just over two week).

D: 6 days (less than a week).

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What answer did you get?

A: You’re way off! You’ll have no chance of stopping an outbreak if you can’t work out how fast it will spread.

B: You’re closer but you’re still dangerously under-estimating how fast the disease will spread.

C: Spot on! Now you know exactly how long it will take before humanity is gone.

D: You’re a pessimist aren’t you? The last human won’t become infected for another 11 days.

How to work it out:The simplest way to work it out is to calculate the number of people infected at the end of each day given the number of people infected at the start and the average number of people they will bite, and so infect. For day one, there will be one person infected at the start of the day (the unfortunate archaeologist) and he will infect three people by biting them. This means that at the end of the day there will be 4 zombies (1 + 3 = 4). Day two starts with 4 infected people, each of which will bite and infect three people. That’s a total of 12 people (4 * 3 = 12). At the end of day two there will be a total of 16 zombies (4 + 12 = 16). If we carry this on, we’ll find that at the end of day three there will be 64 zombies, 256 at the end of day 4 and so on, until at the start of day 17 there will be 4,294,967,296 zombies, and since there’s only 7 billion people on the planet, they will run out of uninfected people to bite somewhere around lunch time.

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.

3. The Fuel Crisis Problem

2 May
maths with zombies

…because everything’s better with zombies!

You hear the first reports on the news that the dead have started to rise and attack the living. You knew this was going to happen and you’re ready. You grab your ‘bug out bag’ and a baseball bat before leaping into your car. The safe house you’ve been carefully preparing and provisioning for the last year is 74 miles away and if you drive fast enough you’ll be there in an hour at the most; then you’ll be safe. As you start your engine you glance at the fuel gauge and realise your room mate’s not only borrowed your car yet again without asking, but he’s also not topped up the tank so it’s only a quarter full. You know your tank holds 11 gallons when it’s full and your car does 27 miles to the gallon. What do you do?

A:I’ve got enough fuel to get there, so I’m leaving the city while I still can.

B:There’s not enough fuel left in the tank. I’ll need to get some more before I head off. It’ll be risky but at least I won’t end up stranded in the middle of nowhere when I run out.

Scroll down to see the right answer…









What answer did you get?

A: Well done, you made the right decision. You must have correctly worked out you have enough fuel to go 74.25 miles before you run out and that’s just enough to get you to your safe house.

B: Oooh, poor choice. You have enough fuel so you should leave immediately. Enjoy fighting off the zombie horde as you waste time trying to find more fuel.

How to work it out: You first need to work out how much fuel you have left in the tank. This is the size of the tank (11 gallons) divided by how much is left in it (1/4) and is 2.75 gallons. Next you need to work out how far you can go on this much fuel. This is done by multiplying the number of miles your car can do per gallon (27) by the amount of fuel you have left (2.75 gallons). This gives you 74.25 miles. Finally, subtract the miles you have to travel from this distance (74.25 – 74). If this number is positive ( as in this case where it’s 0.25), you’ve got enough fuel to get you there. If it’s negative, you haven’t. This would be the case if the miles per gallon was only 0.5 lower: (2.75 * 26.5) – 74 = -1.125, so you’d run out of fuel just over a mile from your safe house. If that were the case, you’d be better selecting option B.

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.