# A Surprise Inside a Surprise Inside a…

Have you ever seen those little wooden dolls that split open to show another little doll inside, then another inside that one? They’re matryoshka dolls from Russia. Matryoshka means “little mom,” and the outside doll is always a woman. If you twist the top half off any doll, inside is a smaller version of herself, until you get down to the last teeny doll. Sometimes even the baby has the pattern, because she wants to look good whenever she actually gets out.

Wee ones: If your matryoshka doll has 4 more dolls inside it, how many dolls are in the set all together?

Little kids: If you’re counting your 7 matryoshka dolls and you’ve counted 2 so far, what numbers do you say to count the rest?  Bonus: If every other doll in a set of 9 is a girl, how many boys are there? (Remember: the biggest matryoshka is always a girl!)

Big kids: If you have 6 dolls and the biggest doll is 6 inches tall, and each doll is 1/2 inch shorter than the next, how tall is the baby?  Bonus: How many ways could 3 doll sets give you 10 dolls, if every set has at least 2? (Don’t worry about the order, just the combinations of sizes.)

The sky’s the limit: If you have a 10-doll set, then get a 9-doll set, an 8-doll set, and so on down to a single wooden baby, how many separate dolls do you have in total? Can you come up with a shortcut to figure it out?

Wee ones: 5 dolls in total.

Little kids: 3, 4, 5, 6, 7.  Bonus: 4 boys.

Big kids: 3 1/2 inches tall. You go down 5 steps to get to the baby, or 2 1/2 inches.  Bonus: Just 4 ways: 2-2-6, 2-3-5, 2-4-4, and finally 3-3-4. All other combinations are just those in a different order.

The sky’s the limit: 55 dolls. This is a “triangle number,” meaning you’re adding a string of numbers that could stack on each other like a pyramid: 1 on top, then 2 under it, then 3 under those. Notice that when you add 1+2+…+9+10, the 10 and the 1 make 11, and so do the 2 and 9, and the 3 and 8…you end up adding 5 11’s, giving you 55.

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