20. The Containment Zone Problem – Part II

12 Sep
maths with zombies

…because everything’s better with zombies!

You have a unit of 600 men under your command. You’ve set up a containment zone surrounding a square of nine city blocks to contain a zombie outbreak, but somehow one of the undead has broken through your line. You give the order for your men to pull back one block. As before, each block is 50 yards long by 50 yards wide and you still need at least two soldiers for every three yards of your perimeter to ensure it’s secure. Do you still have enough men to guard the containment zone once you’ve pulled back, or should you call for reinforcements?

A: With 600 men, I can still maintain a secure containment zone even if we have to pull back.

B: Once we pull back, the perimeter will be too long for my men to guard effectively. I’ll need to call for reinforcements.

Scroll down to see the right answer…

What answer did you get?

A: That’s the wrong choice. While you had more than enough men to secure a 9 city block area, you don’t have enough to hold the larger containment area and because of your decision the city will be lost to the undead.

B: You got it right. You don’t have enough men to secure the larger containment area and you need to call for reinforcements right away!

How to work it out: Again, this is a relatively easy one to work out. First, you need to work out the size of the area you need to secure. Originally, you were securing a square of 9 city blocks. This means it was 3 blocks long by three blocks wide. If your men pull back one block on all sides, this means the area you’ll be trying to secure will be a square of five by five city blocks. As before, this containment zone has four sides, but now each side is five city blocks long, and each block is 50 yards wide. To work out the length of the perimeter, you just need to multiply these three numbers together (50 yards per block by five blocks per side by four sides). This tells you the total perimeter you need to cover is 1,000 yards. Now you the need to work out the total number of men you’d need to adequately cover this larger perimeter. Just as with the smaller perimeter, you need two men ever three yards. This is the same as saying you need 2/3rd of a man per yard, so you divide 1,000 by 3 and the multiply it by 2, giving a total of 667 men (rounded up to the nearest whole man). You only have 600, so now you have to pull back, the only way you can save the city is to call for reinforcements, so you’d better do it 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.


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