I am afraid I am a big fan of the random and "Clever Hans The Maths Horse" would appear to tick all the boxes. In the early 20th century a horse named Hans travelled around Germany performing arithmetic tasks and reading German. If only "That's Life" had been around. The story is also covered in Wikipedia (where the image is from).The "Damn Interesting" website is well worth checking out (even if you aren't interested in mathematical equine adventurers).
Talking about That's Life, who can forget Prince, the dog who says "sausages". He was an inspiration for millions. Check him here on Youtube.
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Horses were initially written off the list of animals with an apparent gift for maths after Clever Hans hoodwinked the scientific establishment in the late 1800s. But a new scientific study has shown that horses DO have the ability to count after all.
Ahem, more here:
http://horseproblems.horsetrainingsuccess.com/2009/04/science-says-horses-can-count.html
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