Extra Terrestrial Puzzle - Solution

The Puzzle:

Extra Terrestrial
Remember the film? Well this puzzle has got nothing to do with it.

On the planet Glogg, the inhabitants are similar to human beings, however they differ in one respect -

they either have 3 heads and the normal amount of arms and legs (known as HEADERS) OR

they have one head and 3 legs and 3 arms (known as LEGGERS).

Last week, I was talking to a group of friends from the planet and between them they had 15 heads and 48 limbs. How many headers and how many leggers were there?




Our Solution:

Headers have 3 heads and 4 limbs (arms & legs).
Leggers have 1 head and 6 limbs.

Between all my Glogg friends there were 15 heads and 48 limbs, so we can say:

Number of Heads: Headers × 3 + Leggers = 15
Number of Limbs: Headers × 4 + Leggers × 6 = 48

Solution:

Headers = 3
Leggers = 6

So there were 3 Headers (9 heads + 12 limbs) and 6 Leggers (6 heads + 36 limbs).


Puzzle Author: Stephen Froggatt

See this puzzle without solution
Discuss this puzzle at the Math is Fun Forum