# Time to Puck-er Up

Every sport uses a different wacky ball or objects, from big orange basketballs to pointy footballs to feathery badminton birdies. But they’re all small compared to the size of the field for that game. So our friend and fan Elliot M. asked, how many hockey pucks can you fit in a hockey rink? Turns out those flat circle-shaped pucks are always 3 inches wide and 1 inch thick. But there’s more than one way to line up those pucks. As you see here, you can line up circles in neat rows and columns, where their centers form squares. But if you line up honeycomb-style so the centers make triangles, you fit more into the same area (instead of rows 1 puck-width tall, it’s the puck width times the square root of 3 over 2 (0.866), based on some very big-kid math).

So on just the 144-foot by 85-foot rectangle of a hockey rink, you can fit 576 rows with 340 pucks the “square” way, or 195,840 pucks…but honeycomb-style you can fit 665 rows of 340 pucks, or 226,143. Next time you line up cupcakes or apples in a box, you’ll know which way works best!

Wee ones: How many blue hockey pucks can you count in the “square” set on the left? Count as high as you can!

Little kids: If a puck is 3 inches wide, how wide is that square set of them?  Bonus: How many more pucks would you need to reach 1 foot (12 inches)?

Big kids: If you have a 12-inch by 12-inch square, how many pucks fit the “square” way?  Bonus: Better yet, what if we stand the pucks on edge in sideways stacks? They’re just 1 inch thick, so how many can you fit across 5 feet? (Reminder: A foot has 12 inches.)