Gold Group sample problems:

A box contains 30 pairs of orange mittens and 20 pairs of black mittens. What is the smallest number of mittens you should take out of the box (without looking) to be sure that you have a pair of mittens of the same color?

A plane leave Anchorage, Alaska and heads straight north. After flying 300 miles, it turns and heads directly west for another 300 miles. Then, the plane turns again and flies directly south for another 300 miles and east for 300 more miles. After this, the plan lands. Would it land at the same spot where it took off?

Brenda the Beaver was cutting three long logs into shorter logs with a chainsaw. She made 50 cuts in total. How many pieces of wood does she have now? (She does not stack logs together when cutting them. The cut logs don’t have to be the same length.)

Blue Group sample problems:

A six-digit number having 1 as its leftmost digit becomes three times bigger if we take this digit off and put it and the end of the number. What is this number?

Suppose in a given collection of 2002 integers, the sum of any 100 of them is positive. Prove that the sum of all 2002 of the integers is positive.

A group of 15 children have gathered 100 nuts. Prove that 2 of them have gathered an equal number of nuts.