# Ducks of a Different Color

When you think of ducks, what color are they in your mind? Are they white with orange beaks, or brownish with green shiny heads, or fluffy gray ducklings? These ducks here are wearing a whole other set of colors. They’re called black-bellied whistling ducks, but we love their pink beaks and the funny white ring around their cute little eyes. Their tummies are hidden underwater, but you can probably guess that those feathers are black. This was Picture of the Day on Wikimedia one day, so we can see them very nicely here — but we can’t hear them. They say these ducks are super loud: as their name tells us, they whistle to call each other. They live in Texas and Louisiana, so if you visit there, keep an eye and an ear out for these feathered friends.

Wee ones: Can you count the ducks in the picture? How many do you see?

Little kids: If 3 of those ducks swim up ahead, how many are left behind?  Bonus: How many ways could the ducks split up into equal groups (with more than one in each group)?

Big kids: If a line of 30 ducks swims along, and every 3rd duck whistles and every 4th duck quacks, which ducks do both?  Bonus: How many ducks don’t make either sound?

Answers:
Wee ones: 8 ducks.

Little kids: 5 ducks.  Bonus: 2 ways: 2 groups of 4 ducks, or 4 groups of 2 ducks.

Big kids: The 12th and 24th ducks.  Bonus: 15 ducks. The 3rd, 6th, 9th, …up to the 30th duck whistle (10 of them), while the 4th, 8th, 16th, 20th, and 28th quack (5 more), because we already counted the 12th and 24th.

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