Brain Teaser

[kcjenkins]

At a recent visit to the reptile house at the local zoo, I counted a total of 27 heads and 70 feet. I was counting snakes, lizards and people and I know that there were exactly twice as many lizards as people. How many snakes did I count?

[jklcpa]

6 snakes, 14 lizards, 7 humans

[kcjenkins]

Very good. Did you calculate it, or google it?

[jklcpa]

calculated, sort of:

1 human for every 2 lizards. Meaning that 1 human & 2 lizards would have a total of 10 legs. 80% of legs would belong to the lizards, since snakes have no legs. 70 legs * 80% = 56 legs for the lizards / 4 legs per lizard = 14 lizards.

14 lizards, so 1/2 # of humans = 7 & the remaining # must be the snakes at 6.

It proved out with the total # of heads at 27.

Surely, someone will post the algebraic formula that is easier than my way. :)

[jainen]

>>4 legs per lizard<<

Not necessarily. Lizards are close relatives of snakes, and they don't all have legs. The Glass Snake, for example, is a common legless lizard (it has movable eyelids so we know it isn't a true snake). It's just the sort of oddity that reptile house managers like to display to generate interest.

[kcjenkins]

I did it this way:

x=people and people have 2 legs and lizards have four legs and there are two lizards, thus 8 legs for every two people legs.

2x+8x=70

10x=70

x=7

Once you have the number of people, and lizards, the snakes are whatever it takes to make the difference in heads.

7H+14H -Snake Heads =27

Snake heads =27-21

[Pacun]

I got my solution this way... I started at the top of the page and then rolled my mouse. My cousing was more creative and pressed page down.

[JohnH]

I like Pacun's method the best.

It's better to use the computer to solve a problem than to strain the brain with all that Algebra.

[bstaxes]

Really liked the problem. My background is math so I solved it using algebra.

S + L + P = 27 snakes, lizards, people number of heads

2P = L twice as many lizards as people

4L + 2P = 70 number of feet

4(2P) + 2P = 70

10P = 70

P = 7

2P = L

2(7) = L

14 = L

S + 14 + 7 = 27

S = 6