Have you ever tried to build a house of cards using a deck of playing cards? Stacking cards is tricky business: you have to stand some of those skinny rectangles up on their edges and lean them against each other before they fall over. Then you rest other cards flat on top and build a new “story” above that, hoping the new cards don’t take the whole house down. Well, an architecture group decided to make a giant house of cards the size of a real building. They used regular building materials to make it strong, but painted the pieces to look like playing cards — and better yet, they built lights into the pieces so the cards flash at night. We’re not sure whether a person could make a house of playing cards this shape that wouldn’t fall over, but luckily this giant one is glued and bolted together.
Wee ones: Playing cards have different shapes to show what “suit” they are: diamonds, hearts, spades and clubs. How many different shapes is that?
Little kids: For any suit, like diamonds, there’s a card for each number from 2 to 10, plus an ace (which is like a 1), a king, a queen and a jack. How many cards does each suit have in total? Bonus: If the 1st floor of this house has 10 cards along one wall, including 2 cards with spades, 3 with diamonds and 1 with clubs, how many heart cards does that wall have?
Big kids: The 1st floor of the house appears to have 10 cards on each of the 2 long zigzag walls, and 6 cards on each of the short walls. How many cards do the 1st floor walls have? Bonus: If each floor has 4 fewer wall cards than the level below it, how many wall cards do the 4 floors have all together?
The sky’s the limit: Suppose that the first level uses all the diamond cards from 2 to 10, and 3 of those cards flash at night; that together those 3 cards have 16 diamonds painted on them; and only the middle card of the three (by value) is an even number. How many possible sets of 3 flashing cards can there be?
Answers:
Wee ones: 4 shapes, or suits.
Little kids: 13 cards. Bonus: 4 hearts, since the other suits cover 6 of the 10 cards.
Big kids: 32 cards (10+6+10+6). Bonus: 104 cards all together: 32 cards on the 1st floor, 28 on the 2nd, 24 on the 3rd, and 20 on the 4th.
The sky’s the limit: There are only 2 possible combinations. The even card can be only a 4, 6 or 8, since 2 and 10 can’t be the middle card. Each of those then needs two odd cards that bring the total to 16. This gives us:
– The 4, 3 and 9 cards. 4, 5 and 7 won’t work because then 4 isn’t in the middle.
– The 6, 3 and 7 cards. 6 can’t be grouped with 9 since then we’re already at 15, nor with 5 because then we’d need another 5 and there’s only 1 of each card.
– Nothing works with 8 because 9 already brings the total past 16, and 8 has to be the middle card.
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.