Archive | April, 2013

2. The Hit And Miss Problem

25 Apr
maths with zombies

…because everything’s better with zombies!

There’s 20 walking dead coming up the street towards your house. You know you need to shoot the zombies in the head to kill them but you’re scared so your aim is off. This means there’s only a 60% chance of you killing a zombie with each shot. What’s the fewest number of shots you will to fire before you are certain to have killed them all?

A: 32.

B: 34.

C: 33.

D: 35.

Scroll down to see the right answer…










What answer did you get?

A: Oh boy, you’re in trouble, there’s still be one zombie left.

B: That’s perfect! All the walking dead are now … err … deader?

C: Oh so close, but there’s still a small chance you’ll miss the last one.

D: That’s one shot too many! This is a zombie apocalypse, you can’t afford to waste ammo like that!.


How to work it out: A 60% chance of killing a zombie means that for every 100 shots you fire, you’ll only kill 60 zombies. If you divide both these numbers by 100, you get the probability of killing a zombie with each shot (in this case it’s 0.6 for every one bullet fired). The minimum number of shots you’d need to fire to make sure all the zombies are killed is calculated by taking the number of zombies (20) and dividing it the probability of killing a zombie each time you fire your gun (the 0.6 you worked out above). 20/0.6 is 33.3333. However, you can’t fire 0.3333 of a bullet. If you round it down to 33 shots, there’s a small possibility that you won’t kill the last zombie (and when you’re trying to survive in a zombie apocalypse you don’t want that!), so you’d need to round up to 34 shots to make sure you’ve got the lot. Any more shots than that would just be a waste of precious ammo.

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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1. The Reload Problem

18 Apr
maths with zombies

…because everything’s better with zombies!

There are fifty zombies staggering towards you. You have a gun that holds six bullets and it’s fully loaded (after all there’s zombies out there so you’ll make sure you’re prepared before stepping out of your safe house). Assuming you don’t miss with any of your shots (and you’d better not or they’ll get you!), how many times will you have to reload your gun before you’ve kill all of them?

A: 6.

B: 7.

C: 8.

D: 9.

Scroll down to see the right answer…










What answer did you get?

A: That’s not nearly enough there’s still going to be loads of zombies coming at you.

B: You’re getting closer but there’s still be two dead men walking.

C: Spot on, and you’ll still have four bullets left in case you run into any more.

D: Whoa, calm down there – that’s too many reloads. Don’t get so trigger happy, you can’t afford to waste your precious ammunition.


How to work it out: You’re going to have to fire 50 shots to kill 50 zombies (we’ll cover the subject of what happens if you aren’t a perfect shot in a later problem). You’ve got six bullets in your gun already, so that’s 6 zombies dead before you have to reload meaning there’s 44 left (50 – 6). Each time you reload the gun, you put six bullets into it, so it we divided 44 (the number of bullets needed to kill the rest of the undead horde) by 6 (the number of bullets the gun can hold), we get 7.333. Since you can’t load a gun 0.333 times, this number needs to be rounded up to 8, and so we arrive at the answer. If there had been 48 zombies, the answer would be (48 – 6)/6, which is 7 (there’s no decimal fraction so there’s no need to round the answer up). If there were 52 zombies, the answer would be (52 – 6)/6, which is 7.6667, so again you’d need to reload your gun 8 times but this time you’d only have two bullets left in the gun by the time they’re all dead.

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.

16 Apr
maths with zombies

…because everything’s better with zombies!

Maths is boring, right? Well, quite frankly, yes. Especially when it’s all about how long it takes train A to pass train B given their relative speeds. So, so boring and not exactly relevant to real life, is it? The thing is, it needn’t be this way. Maths problems can be made both much more interesting and more relevant to everyday life. How? By adding zombies! Zombies make everything better and of course, as we all know, one day there will be a zombie apocalypse. When that happens the maths problems posted on this blog are the ones you’ll need to be able to do if you want to survive in a world where the dead walk again…

…This is the world of Maths With Zombies!

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I’ll post the first zombie-related maths problem on Thursday the 18th of April 2013 at 15:00 (UK time), and then add a new one at the same time each week for the foreseeable future. There’s no prizes or anything on offer, I’m just posting them for fun. If you are so minded, you can also view them as useful training exercises for the inevitable zombie apocalypse that will one day bring humanity to its knees. After all, that’s when being able to do Maths With Zombies will really come into its own!

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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). 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.