Archive | August, 2013

18. The Zombie Horde Problem

22 Aug
maths with zombies

…because everything’s better with zombies!

You’re out foraging for food when you turn a corner and find a mass of zombies staggering down the street towards you. Climbing onto a burned out car, you can see that the horde stretches back for five city blocks, each of which is 88 yards long, and that they are moving at 3 miles an hour. You look round for somewhere to hide but the only shelter that’s close enough is an abandoned tank. You climb inside and lock the hatch just as the first of the zombies reach you. If you keep very quiet, they won’t know you’re there and they’ll all walk right passed. If, however, they realise you are there, they’ll surround the tank and you’ll never be able to get out. Being a tank, there’s no way for you to see outside without opening the hatch to take a look, yet night is falling fast and if you stay in the tank too long, you won’t be able to get back to your safe house before it gets dark, so every minute counts. How long will it be before it’s safe for you to open the hatch again? (HINT: There’s 1,760 yards in a mile.)

A: 4 minutes.

B: 5 minutes.

C: 6 minutes.

D: 7 minutes.

Scroll down to see the right answer…









What answer did you get?

A: Oh no! You opened the hatch a minute too soon, meaning there were still zombies all around you. Now they know you’re there, you’ll never get out alive.

B: Spot on! You opened the hatch just as the last zombie has shuffled passed, meaning you can escape back to your safe house before night finally falls.

c: You stayed in the tank a minute too long. You’ll be safe from the zombie horde, but you might not make it back to your safe house before it’s dark.

D: Seven minutes? You’re way out. You’ll never make it back to your safe house in time. Looks like you’ll be stuck in the tank all night.

How to work it out: The first thing you need to work out is how long the horde of zombies is. Each city block is 88 yards in length and the zombies stretch for five blocks so the whole zombie horde is 5*88 yards long. This works out at 440 yards. This means that the last of the zombies are 440 yards away when you close the hatch on the tank. Next, you need to work out how long it will take all the zombies to stagger passed you. To do this, the first thing you need to do is convert the speed from miles an hour to yards a minute. This is done by multiplying the speed in miles an hour (3) by the number of yards in a mile (1,760), to give a speed of 5,280 yards an hour. This number is then divided by the number of minutes in an hour (60) to work out the speed in yards per minute. When you do this, you find out their speed is 88 yards a minute. You can now divide the number of yards the last of the zombies have to travel (440 yards) by this speed (88 yards a minute) to find out that it will take 5 minutes for the last of the zombies to pass your hiding place.

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.

17. The Tank vs Motorcycle Problem

15 Aug
maths with zombies

…because everything’s better with zombies!

You’ve heard about a safe zone which has been set up and you figure getting there is your best chance of surviving the zombie outbreak in your country. The bad news is that it’s 125 miles away. You have two transport options: a motorbike and a tank. The motorbike‘s much faster and you’ll be able to travel at 60 miles per hour. However, it’s also much more dangerous and there’s a one in six chance you’ll get grabbed by a zombie during each hour you’re on the road. The tank’s a lot slower and can only travel at 7 miles per hour, meaning you’ll be on the road for longer, but it’s also much safer and there’s only a one in fifty chance of a zombie getting you during each hour you are travelling. Which transport option offers you the best chance of getting to the safe zone in one piece?

A: The tank’s slower but safer, so it’s the best option.

B: While the motorbike is less safe, you’ll get there quicker, so overall it’s the best option.

Scroll down to see the right answer…









What answer did you get?

A: Bad choice! There’s a 35.7% chance of you getting caught by a zombie before you reach the safe zone if you choose to travel by tank. This means travelling by tank is marginally more dangerous than travelling by motorbike.

B: Well done, you made the right choice. With a 34.7% chance of getting grabbed by a zombie before you get to the safe zone, the motorbike is safer than the tank.

How to work it out: The key to this problem is working out how long it will take to reach the safe zone using each mode of transport. This is done by dividing the distance you need to travel (125 miles) by the speed of each vehicle. For the tank, this is 125/7 and it means you’ll be on the road for 17.86 hours. For the motorbike, it’s 125/60, meaning you’ll get to the safe zone in 2.08 hours. Now, you can work out the cumulative probability that you’ll get caught by a zombie for each one. For the tank, it’s 1/50 per hour or, if you convert this into a percentage by dividing 1 by 50 and multiplying it by 100, 2%. To get the cumulative probability, you multiply this value by the length of time the journey will take (17.86 hours), which gives you a total chance of falling victim to a zombie before you get to the safe zone of 35.7%. For the motorbike, there’s a 1 in 6 chance of a zombie getting you per hour, or if converted into a percentage, 16.67%. When you multiply this by the time it would take you to get there on the motorbike (2.08 hours) this gives you an overall probability getting killed by a zombie before you get there of 34.7%. Despite the fact there is a far greater risk of you getting caught by a zombie in each hour, the motorbike’s much faster speed means you spend less time on the road, so overall it’s marginally safer.

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.

16. The Wall Problem

8 Aug
maths with zombies

…because everything’s better with zombies!

There’s been an outbreak of the zombie disease in Glasgow and Scotland is being over-run. The latest surveillance mission spotted a horde of zombies heading south. They’re currently 125 miles away and are moving at a speed of 3 miles per hour. Scotland is lost and the best way to protect the rest of Britain is to build a defensive barricade on the ruins of the ancient Roman wall which was last used over 1,600 years ago. 750 people can build a one mile long section of ten foot high wall in a day but the wall will need to stretch the entire 73 miles from one side of Britain to the other along the border between Scotland and England if it’s going to keep the zombies out. What’s the minimum number of people you will need to recruit to ensure the wall’s completed before the zombie horde gets to it?

A: 7,884

B: 15,768

C: 31,536

D: 54,750

Scroll down to see the right answer…









What answer did you get?

A: With 7,884 people, you’ll only get 18 and a quarter miles of wall built in time and that will hardly keep the zombies out, will it?

B: With 15,793 people, you’ll only get half the wall built before the zombies get there, and half a wall is little better than no wall at all.

C: That’s right. with 31,536 people you’ll just get the last brick in place as the zombies reach the wall.

D: With 54,750, you’ll get the wall built with plenty of time to spare, but maybe all those extra people could have been doing something else instead.

How to work it out: The first thing you need to work out is how long it will take the zombies to reach you. If you divide the distance they have to travel (125 miles) by the speed they are moving at (3 miles an hour), you’ll find it will take the zombie horde 41.67 hours to reach you. This means you have to have the wall finished in 41.67 hours, or (if we divide this by the number of hours in a day – 24) 1.74 days. Next, you need to work out how many people you would need to finish the wall in this time. 750 people can build one mile of wall in a day, but the wall needs to be 73 miles long. If you multiply these two numbers together, you’ll find that 54,650 people could build the whole wall in one day. Except you have 1.74 days and not just one day, so you need to divide this number by 1.74 to get the number you need to complete the wall before the zombies get there, and this is 31,536 people. That’s a lot of people, so you’d better start recruiting them right away!

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.

15. The Out-Running Your Friends Problem

1 Aug
maths with zombies

…because everything’s better with zombies!

There are 37 zombies chasing you and your friends. The zombies are those pesky new fast ones and they’ll quickly catch whoever’s moving slowest. Each time one of your friends gets caught, 3 zombies stop to feast on their brains. How many of your friends do you have to out-run before all the zombies are too busy eating other people to chase you, meaning you can finally get away?

A: 12

B: 13

C: 14

D: 15

Scroll down to see the right answer…









What answer did you get?

A: With only 12 friends down, there will still be 1 more zombie chasing you, so you’ll still have to out-run 1 more friend to escape.

B: Perfect. You might have lost 13 friends, but at least you got away from the zombies

C: That’s one more friends than you need to out run. You did get the maths wrong, didn’t you?

D: Humm, you do like your friends, don’t you?

How to work it out: This is a nice simple one. Each time the pursuing zombies catch someone, the number chasing you goes down by 3. This means all you need to do is divide the number of zombies by 3. In this case, with 37 zombies chasing you, when you divide this by 3 you get 12.33. This means that after 12 of your friends have been caught, there will still be one zombie chasing you (it’s the 0.33), Therefore, one more of your friends has to get caught before you are finally free to escape, so the total number of friends you have to out-run it 13.

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.