It’s hard to look at that picture without feeling dizzy. How many people are out there? There are actually 8 women dancing on the stage, but each one is wearing an outfit that’s half white, half black. The outfits are mirror images of each other. So when 1 woman steps forward with her right leg along with the next woman’s left leg, those 2 legs are the same color. Together they look like a new person, but with no head, since of course that “person” is really half of 2 people. Weird!! If you watch the video, the split people trick our eyes in all kinds of ways; sometimes they look like they’re floating in the air. If you and your friends can find pants like these, you can try these tricks, too.
Wee ones: How many black legs can you count? Count them as high as you can!
Little kids: For the woman all the way on our left in the picture, which of her legs is white: her right, or her left? Bonus: How many all-black pairs of legs next to each other does the group make?
Big kids: If you have 30 people out there, again with the ends the way they are here, which leg is black on the 13th person counting from the DANCERS’ left? Bonus: If there were 12 women out there, how many all-white pairs of legs next to each other could they make, assuming the end people had white on the outsides as they do here?
The sky’s the limit: How many all-white pairs of legs next to each other would 31 women make? Can you figure out a quick rule that works for any even or odd number of dancers?
Wee ones: There are 8 in total — 1 per real person!
Little kids: Her right leg. Imagine her turning around to face the curtain just like you… Bonus: 4 pairs.
Big kids: The right leg, the same as on the 1st person and all odd-numbered people. Bonus: Just 5. They’d have 6 full pairs of white legs, but with the last pair split on the ends; it wouldn’t make a “person.”
The sky’s the limit: 31 women would make 15 complete white pairs, since 30 people would make 14 white people, and that 31st dancer would complete the 15th. For any number of dancers, the answer for complete white pairs is the number of dancers minus 1, then cut in 1/2, then rounded down if you get a fraction. Try it with other numbers!
Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking before she could walk, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.