Everyone loves a great waterslide – and so do ducks! At the South Carolina State Fair, someone set up a waterslide and let 6 baby ducks play on it, as we see in this video. 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: If there are 6 ducklings total and 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?
Answers:
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.
