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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