Problem 1: Can Batman catch the Riddler in time before it's to late?

Batman has been imprisoned by the Riddler. To escape he must find the quickest way to move the tower of plutonium disks from one post to another so that the disks have the same arrangement as on the original post. He may move only one disk at a time. What is the minimum number of moves he must make in order to move the ten disk tower and have it appear the same?

Problem 2: Can Batman Solve the Crime?

The Riddler has left a clue for Batman to follow at the scene of each crime. These are the clues that Batman has found:

(1) There is a 1 in the thousands place.

(2) The digit in the tens place is 9 times the digit in the thousands place.

(3) Multiply the digit in the thousands place by 2.

(4) The digit in the ones place is a hand without a thumb.

(5) The digit in the hundreds is 2 less than the number in the tens.

Solve the riddle to find the number and help Batman stop the Riddler.

Problem 3: Ice Cream, Ice Cream, I Scream for Ice Cream

An ice cream stand has nine different flavours. A group of children come to the stand and each buys a double scoop cone with two flavours of ice cream. If none of the children choose the same combination of flavours, and every different combination of flavours is chosen, how many children are there?

            FLAVOURS

            1          Vanilla

            2          Maple

            3          Chocolate

            4          Tiger

            5          Raspberry

            6          Strawberry

            7          Coffee

            8          Moon Mist

            9          Cherry Vanilla