# Did Grandpa count correctly? Another Grandpa Mystery

Grandpa just returned from a long trip. He started telling me about his adventure in a wild place.

" I saw animals", he said. "Three different kind"

"Just for fun I counted their limbs"

"You mean legs" I interrupted

" Yeah whatever. There were 26 total animals of 3 different kind. And I counted 26 legs for the 26 animals.

The total number of first kind of animal was 8 times the second kind and 2 times the third kind.

Can you guess what kind of animals I saw and how many of each were there?

And where was I?

By the way, there were no one legged or disabled animals there, just to be clear

Did he count correctly?

Well, I'd say Grandpa was in

Australia

And he saw

16, 8 and 2 animals of three types. Why?

assume the least number was 1. That makes the largest number 8 and the middle 4. That's 13, so we should double each number for 16, 8, 2.

Of which

the 16 can't have two legs (more than 26) and no one legged animals, so they have 0 legs (snakes?)
The 8 can't have 3 legs, because the 2 would have to be one legged, so the 8 have 2 legs/limbs. This could be a wingless bird like a Kiwi. (ok, it has wings but they are so small they are invisible and Grandpa wouldn't have seen them)
The 2 have 5 limbs, therefore. Which a Kangaroo is considered to have, counting it's tail (hence Australia)

• Also, rot13[Ur fnj 26 navznyf, 16 bs juvpu jrer fanxrf. Vs gung qbrfa'g qrfpevor Nhfgenyvn V qba'g xabj jung qbrf.]
– Jafe
Commented Oct 1, 2018 at 11:06

Ok, so he said he counted 26 animals

We have that

• number of type 1 = n
• number of type 2 = n/8
• number of type 3 = n/2

n + n/8 + n/2 = 26, therefore n = 16

so he saw:

• 16 of type 1
• 2 of type 2
• 8 of type 3

But what were they?

He saw 16 type 1's, and saw no one legged animals; if type 1 had 2 legs, the minimum allowable, he'd have seen 32 limbs; too many already. So, type 1 has no legs, must be a snake or fish.

from that we have

(2*x)+(8*y) = 26. Logical numbers are 2 and 4; lets plug them in: 2*4 + 8*2 = 24 thats too low; but if we add 2 legs to either we blow it out...

but he originally said

limbs, so thats not necessarily in pairs... 2*5 + 8*2 is just right

Thus, he saw

16 snakes, fish or other zero-limbed creatures
2 five-limbed creatures. I'm going with starfish, but spider-monkeys with prehensile tails could be another contender
8 two-limbed creatures, this could be anything; flamingoes, chickens etc.

• thanks el-guest; man i'm struggling with spoilerised paragraphs; what a pain! Commented Oct 1, 2018 at 0:18
• Great Logic @crcroberts. But "Where was I?" was the question he asked.
– DrD
Commented Oct 1, 2018 at 11:46