A Very Cool Sandwich

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?

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.

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