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.


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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