For The Mathematically Inclined

Problem 1
A mystery number has two digits. It is an odd number less than 50 but greater than 45. How many possible mystery numbers are there?

Problem 2
Hank the hot dog vendor is trying to buy the same number of hot dogs and hot dog buns. Hot dogs are sold in packages of 6. Buns are sold in packages of 10. Whatâ€™s the smallest number of packages of hot dogs and of buns that Hank can buy to have a matching number of each?

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Problem 1
You are going to visit your grandmother on Mother's day. You want to give her two cakes. However, to get to her house you must cross seven bridges. At each bridge is a troll who demands Â½ of all of your cakes as the price to pass. However, this troll, being a nice troll, feels bad and gives you back 1 of the cakes that he took.How many cakes must you leave with to be able to give your grandmother 2 cakes?

Problem 2

When Dev was six years old he hammered a nail into his favorite tree to mark his height. Five years later at age eleven , Dev returned to see how much higher the nail was. If the tree grew by ten inches each year, how much higher would the nail be?