When you trick-or-treat for Halloween, there are all kinds of candy you can get. But deep down they all have the same ingredients, just mixed in different combinations. Chocolate alone gives us zillions of choices. There’s plain chocolate, which comes in flat bars and in chunks like Hershey Kisses. But some chocolate treats mix in caramel, like round Rolos or thin Ghirardelli squares. Some have soft spongy nougat inside, like 3 Musketeers. But then some candy has nougat and caramel, like Milky Way, and Snickers and Baby Ruth throw in nuts on top of that. Then we have a whole set of candy bars that mix in crisped rice.
So we’ve mapped this out using one of our favorite math shapes, the Venn Diagram. Each circle contains a set of things that have something in common, like chocolate or nuts. Where 2 or more circles overlap, the treats in that space live in all the circles involved – they have all those ingredients. Find your favorites, and if we missed them, you can figure out where to put them!
Wee ones: Which has more squares, a chocolate bar with 8 squares or a chocolate bar with 10?
Little kids: If you have 10 pieces of candy and 7 of them have caramel, how many don’t? Bonus: If the non-caramel pieces have nuts along with 6 of the caramel ones, how many pieces have nuts?
Big kids: If in total 20 of your treats have caramel and 20 have nuts, but 5 of those pieces have both ingredients, how many pieces do you have in total? Bonus: If you then get 23 more treats, how many of them at most can be plain if they double your caramel-only total?
Wee ones: The bar with 10 squares.
Little kids: 3 pieces. Bonus: 9 pieces.
Big kids: 35 pieces. You still have 20 in total with caramel, some of which happen to have nuts, and then you have another 15 nuts-only pieces. Bonus: At most 8 pieces, since 15 of them will need to have caramel.
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.