zoo story

[MattcAnderson]

Hi Math people,

I have another fun math problem. This one should not be a challenge for some of you. A man has a conversation with a zookeeper -

Man: How many birds and how many beasts do you have in your zoo?
Zookeeper: There are 30 heads and 100 feet.
Man: I can't tell from that.
Zookeeper: Oh, yes you can!

Can you?

Regards,
Matt

[science_man_88]

Originally Posted by MattcAnderson

Hi Math people,

I have another fun math problem. This one should not be a challenge for some of you. A man has a conversation with a zookeeper -

Man: How many birds and how many beasts do you have in your zoo?
Zookeeper: There are 30 heads and 100 feet.
Man: I can't tell from that.
Zookeeper: Oh, yes you can!

Can you?

Regards,
Matt

unless you count things with two heads or some of the animals have their heads cut off,the answer has to be 30. another thing that comes to mind though is how many ways this could possibly be brought about though I thought of using 31 and having 30 bipeds and a decapod edit: 5 decapods and 25 bipeds works, edit2: so should 6 arachnids an insect and 23 bipeds, I'm clearly stupid.

[CRGreathouse]

Originally Posted by MattcAnderson

Man: How many birds and how many beasts do you have in your zoo?
Zookeeper: There are 30 heads and 100 feet.
Man: I can't tell from that.
Zookeeper: Oh, yes you can!

I'm supposing that birds have one head and 2 feet, while beasts have 4 feet and one head. So birds + beasts = 30 and 2*birds + 4*beasts = 100, hence birds + 2*beasts = 50. Subtracting the first from this gives beasts = 20 and we can back-substitute to find the number of birds.

Hmm. Somehow I was hoping this would have been one of those logic puzzles where there isn't enough information but then knowing that the man couldn't figure it out gives you just enough information.

[retina]

Originally Posted by MattcAnderson

There are 30 heads ...

Too much bureaucracy.

Originally Posted by MattcAnderson

... and 100 feet.

Give a man enough rope ...

[Mini-Geek]

I, too, am assuming that all birds have 2 feet and all beasts have 4.
h_total = 30
30 = h_birds + h_beasts
h_birds = 30 - h_beasts
2*h_birds + 4*h_beasts = 100
2*(30 - h_beasts) + 4*h_beasts = 100
2*h_beasts = 40
h_beasts = 20
h_birds = 10