by
Erik Oosterwal
Each human has 2 eyes and each horse has 2 eyes, so there were a total of
11 horses and people.
Let P = number of people and H = number of horses, then
H+P = 11 and P = 11-H
There were a total of 34 legs. Horses have 4 legs, people have 2, so we can
write
4H + 2P = 34
If we replace the value of people in the second equation with the value of
people from the first equation we get:
4H + 2(11-H) = 34
We can solve the rest fairly quickly:
4H + 22 - 2H = 34
4H - 2H = 12
2H = 12
H = 6
Plugging the value of horses back into the first equation we get:
P = 11-H = 11-6 = 5
There are 5 people and 6 horses.
In the second part we have a bit more to worry about, but we are provided
with additional information. Let P = the number of people, H = the
number of horses, W = the total number of wildlife, O = the number of ostriches,
and D = the number of dingoes.
2P + 2H + 2W = 52 (eyes)
We know there are 5 humans and 6 horses so we get:
2(5) + 2(6) + 2W = 52
10 + 12 + 2W = 52
2W = 30
W = 15
The total number of all wildlife is 15 animals.
The 5 humans, 6 horses, and 15 wildlife have a total of 74 legs. If we subtract
10 legs for the 5 humans we are left with 64 legs, and if we subtract 24
legs for the 6 horses we are left with 40 legs. We were told that there
were twice as many 4 legged creatures as there were 2 legged creatures so
we are led to believe that O+D = 15, D=2(O), therefore 3(O) = 15, O=5 and
D=10.
However, with 5 ostriches and 10 dingoes we should have 50 legs, but we have
only 40 legs left for all the wildlife. Obviously either the numbers
are wrong or some clue to the puzzle has been left out (on purpose).
If we start with the total number of legs left, we get 2(O)+4D=40, D=2(O),
therefore 2(o)+4(2(O)) = 2(O)+8(0) = 10(O) = 40 and O=4, D=8. This leads
us to one conclusion, of the 15 animals, 4 were 2 legged ostriches, 8 were
4 legged dingoes, and the remaining 3 were 0 legged snakes.
Ok, ok, I didn't mention snakes in the original puzzle, but sometimes you
have to think outside the box a bit. I suppose you could have claimed that
there were 5 ostriches and 10 dingoes and that the dingoes were each
missing a leg, but the puzzle did state "4 legged dingoes", didn't it?
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