Everyone loves a great waterslide: it’s fun to swoosh down and make a giant splash at the bottom. But why should we humans have all the fun? Ducks love water — and it turns out they love water slides, too. At the South Carolina State Fair, someone set up a waterslide and let 6 baby ducks play on it. Ducks are great swimmers, thanks to waterproof feathers, lots of body fat that helps them float, and webbed feet that paddle fast. But as we see in this video, they’re happy with 1-inch-deep water, too. It looks like there are snacks at the top of the ramp as a bonus treat. If only we humans could have one of these in our living room…
Wee ones: Who has more feet, you or a duck?
Little kids: There are 6 ducklings waddling around on the waterslide. If one’s on the slide and one’s waddling up the ramp, how many are left snacking ? Bonus: How many of those webbed feet do the 6 ducklings have altogether? Count up by 2s if you want!
Big kids: If each of the 6 ducklings takes 4 turns, how many duck-slidings happen in total? Bonus: The video lasts about 30 seconds, and the 6 ducklings each slide once. If they took their turns evenly spaced, with one starting right at 0 seconds and the last one at 30 seconds, how many seconds apart did they start their turns?
The sky’s the limit: If these 6 ducklings are named Quinn, Quan, Quickie, Quackie, Queenie and Quipper, how many ways can they line up so that Quinn always slides first?
Wee ones: Both people and ducks have 2 feet, so you have the same number!
Little kids: 4 ducklings. Bonus: 12 feet.
Big kids: 24 slidings. Bonus: 6 seconds, because after the 1st duck the remaining 5 ducks split the time into 5 equal chunks. This “do you count the start?” issue is called the “fencepost problem.”
The sky’s the limit: 120 ways. If Quinn always slides first, then only 5 ducks have to rotate their line-up. You have 5 choices for the 2nd duck, then once he/she is chosen, for each of those 2nd-sliders you have 4 choices for the 3rd duck, giving you 5 x 4 combinations. Then for each of THOSE combos, there 3 choices for the next slot, and so on, giving you 5 x 4 x 3 x 2 x 1 = 120 possible line-ups.