What if we made climbing stairs more fun? One company turned a stairway in a subway station into a real 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. 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.)
Answers:
Wee ones: They are in sets of 2 or 3. 3 keys make the bigger group.
Little kids: 10 feet: 2 for the man, 4 + 4 for the dogs. Bonus: 6 feet.
Big kids: 34 notes. Bonus: 1,000 people, since 400 more people (2/3 of 600) walked them.
The sky’s the limit: 32 combinations. Since the 5 right-foot steps are always white, all you need to worry about are the 5 left-foot steps, each of which can be black or white. There are 2 choices for the 1st left step, and for each of those, 2 possibilities for the 2nd left step…so in the end you have 2 x 2 x 2 x 2 x 2 possibilities, or 32.
