August 2 is Ice Cream Sandwich Day! This treat was invented in the early 1900s in New York City, when an ice-cream cart guy mashed vanilla ice cream between two thin cookies. Then in 1981 came the chocolate-chip Chipwich. As New York Times writer Ligaya Mishan found out, these days New York City has sandwiches made with coconut-jackfruit ice cream, ice cream flavored with grown-up liqueurs, and open sandwiches with no top layer at all. So feel free to mix and match your own cool treats!

*Wee ones:* If an ice cream sandwich has a cookie, then a layer of ice cream, then another cookie, how many layers does it have?

*Little kids:* How many complete sandwiches can you make if you have 7 chocolate chip cookies handy? *Bonus:* How many would you need to make 7 *sandwiches*?

*Big kids:* If you have 4 kinds of cookies — sugar, Oreos, chocolate-chip, and oatmeal — and 4 flavors of ice cream — coconut, mint, peanut butter, and pistachio — how many wild cookie-ice cream sandwich combos can you make? (Assume each sandwich uses 2 of the same cookie.) *Bonus:* When did the Chipwich, born in 1981, have its 25th birthday?

Answers:

*Wee ones:* 3 layers.

*Little kids:* Just 3, since that will use 6 cookies; you’d need 8 to make 4 sandwiches. *Bonus:* 14 cookies (2 cookies apiece).

*Big kids:* 16 kinds, since each of the 4 pairs of cookies can go with any of the 4 flavors. *Bonus:* In 2006.