The Heads and Legs Paradox

This heads and legs paradox has been famous from grade school to mid-schoolers.  The problem is something about determining the number of animals given the total number of their heads and legs or feet. For grade schoolers, they can solve it by trial and error until the given condition is achieved. For middle schoolers, they used algebra to solve this. Assign unknowns, generate equations and solve it. For better understanding, here is an example.

paradox

Mang Kanor is breeding Chickens and Goats. He asked his nephew Ben to count the number of heads of these animals. He also asked Loi to count the total number of legs these animals have. Ben reported that he counted 40 heads, Loi counted 110 legs. How many chickens Mang Kanor have?

Solution:

Let C be the number of chicken

Let G be the number of goats

Since the number of heads is 40,

Heads of Chicken + Heads of Goats = 40

1 Head of Chicken = 1 Chicken(C )

1 Head of Goat = 1 Goat (G)

C+G=40 (1)

Since there are 110 legs,

Legs of Chicken + Legs of Goat = 110

1 Chicken(C ) has 2 legs

1 Goat (G ) has 4 legs

Goats (4 legs per goat) + Chicken(2 legs per chicken) = 110

4G+2C=110 (2)

(1) and (2) are the smart way to solve this paradox. These are two equations in two unknowns.

We can rewrite (1) as G=40-C

Substitute this to (2)

4G+2C=110

4(40-C)+2C=110

160-4C+2C=110

-2C=-50

C=25

Therefore, there are 25 chickens. Since there are 40 animals, there are 15 goats. Try to check if the number of legs will equal to 110.

 

 

 

Dan

Dan

Blogger and a Math enthusiast. Has no interest in Mathematics until MMC came. Aside from doing math, he also loves to travel and watch movies.
Dan

Latest posts by Dan (see all)

You may also like...

2 Responses

  1. Wenona says:

    I’ve been exploring for a little for any high quality articles or blog posts on this sort of area . Exploring in Yahoo I at last stumbled upon this web site. Reading this info So i’m happy to convey that I’ve a very good uncanny feeling I discovered just what I needed. I most certainly will make certain to don’t forget this website and give it a glance on a constant basis.

  2. Hello there, simply became alert to your weblog through Google, and found that it is truly informative. I am gonna watch out for brussels. I will be grateful in the event you continue this in future. Numerous people might be benefited from your writing. Cheers!

Leave a Reply

Your email address will not be published. Required fields are marked *