It's so tempting to be lazy and take the elevator instead of walking up the stairs. But what if we made the stairs more fun? To find out, the car company Volkswagen turned a stairway in a subway station into a real working piano keyboard. They stuck sensors and speakers under the floor, painted the stairs like black and white piano keys...and boom, each time you step on a stair, it plays that musical note. Suddenly people wanted to walk on the stairs, then when others heard the music, they wanted to try it. 66% more people started taking the stairs!
Wee ones: How many black piano keys are together in a little group? Which set is bigger?
Little kids: When the guy with 2 dogs ran up the stairs, how many feet all together made music? Bonus: If 1 dog stopped to sniff a piano key, how many feet would still be on the move?
Big kids: If there are 17 steps in total, and you run up, then back down, how many notes do you play? (Assume you hit every step exactly once on each trip.) Bonus: 66% is an extra 2/3 of people. If before the experiment 600 people used to take the stairs each day, and it increased by 2/3 of that, how many people took the stairs after the piano setup?
The sky's the limit: If someone runs up the middle of the stairs and taps 10 steps total, and his right foot always hits a white key but his left foot can hit a black key on any step, how many possible color patterns of black and white keys can he step on (assuming he starts on the right foot)? (Don't worry about which black or white key, just the pattern of black vs. white.)
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