When I was a kid, my brother told me that animals can’t count. He told me that researchers utilize this fact. They will build a blind near an animals den then enter in a group of two. Then one person will leave. The animal (who cannot count) believes that there is no one behind the blind and begins to behave naturally.
We were young at the time so I’m not sure if there is any truth to this story.
Can animals count?
You might find this book interestin, although I’m not sure if it actually covers whether or not animals can count. The Math Instinct : Why You’re a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs)
I’ve seen studies showing that chimps can be taught to do simple math, but IIRC, they tend to get confused once the numberrs get higher than 5 or 6.
Alex, the grey parrot, can count up to six. This article claims that pigeons can count up to fifty.
My grandmother’s dog could count up to three. He knew that when my mother came to visit, she would give him three treats. He wouldn’t stop pestering her until he’d gotten the third, and no, it wasn’t the scent: she once experimented by leaving the third treat in the car. He ate the two she gave him and then begged and bumped her until she got up and went to get the third. After he got it, he would leave her alone.
My dog seems to be able to go up to three, we do a trick where I count to three then he barks, but you know animals are so good at picking up other clues like facial jesters, I did it from behind and he got it.
I really have trouble thinking animals can actually count, even though my dog does the trick well, even if I turn around. It seems to me anything involving counting the animal is picking up on jesters the person gives him
You have clowns on your face? You might wanna see a doctor about that! 
*snipping and bolding mine for emphasis.
ISTR a National Geographic article that said octopuses can count to eight.
Some people just look . . . funny.
You never heard of Counting Crows? Where do you think the name came from?
I don’t know about counting but rabbits have been known to multiply.
Funny that several people have said this. I’ve always jokingly said that dogs can count to three because I had two dogs that would let me clean three of their feet before coming in the house and then assume I was done and try to bolt off. Try as I might to tell them they had four feet, they always thought we were done after three.
I believe my cats can distinguish 2 and 3 for similar treat-related reasons; if I give one cat 2 treats and the other 3, the 2-treat cat knows it and wants another. If I give them both more–say 5 or 6 each–they don’t notice the difference, so I don’t think they can count that high. I haven’t actually tested them on 4.
Our late black-and-white cat Kami was left at home for several weekends in a row. He got visibly nervous and clingly starting Friday afternoon of the first weekend when this did not happen, even though the obvious warning signs of suitcase packing, etc, did not occur. The simplest explanation I can see is that he was able to count off seven days.
Scientific American Frontiers had an episode about animal intelligence.
Wild monkeys can count - researchers went out when they knew a monkey was watching, and would drop fruit one at a time into two buckets - one or the other bucket got more. They repeated this several times with several monkeys and without exception the monkey would make a bee line for the one with more fruit.
Not being able to see the fruit, they couldn’t have determined which had ‘more’ without having counted as the researcher dropped the fruit in.
Alright, boxes, not buckets:
It’s either that or some sort of patterning. My dogs all wait by the bed on weekday mornings for my husband to vacate it so they can jump up into his spot. They don’t do that on the weekends-- they know my husband sleeps in, so there’s no point in waiting by the bed.
I think the plural for octopus is octopieces. Or is it octopopi? 
Thank you for your very interesting responses. It is clear that some animals can count to a limited extent. I am still curious about the story mentioned in my original post. Are some animals so mathematically challenged as to be fooled into thinking the no one is behind a blind when two men enter and one leaves?
Maybe they’re fans of Thunderdome and want to sidle up and get a better look at the body.
I’d wager that it isn’t counting at all, but hearing. A dog’s hearing is good enough to hear traffic blocks away, and on days when there’s less traffic, a dog might learn that it’s sleep-in day.
So the question is, do your dogs do this on holidays where your husband sleeps in, and do you live close enough to a busy road that they might notice the difference in traffic on weekends?
It’s like the rats-in-the-maze experiment, I believe. Put rats in a maze and they’ll learn the way through it eventually. Are they following the scent of cheese, or the colors of the walls? We humans assume why the rat can learn this, attributing it to intelligence or counting or spatial reasoning, never realizing that the rat is listening to the sound of the floor under its claws. (I can’t remember where I read about a controlled rat-maze experiment where they fooled the rats by filling the maze with sand.)