A quilt was sewn together originally with unit square pieces. Unfortunately, the eight middle square pieces were damaged and had to be removed. Can the quilt be repaired with a cut along the square grid for two parts to be sewn into a new quilt without holes?

In a certain country, every citizen has a unique 4-digit identification number. The sum of the digits of each number is also unique. How many citizens are there in this country?

What is the maximum number of regions that can be formed by N intersecting lines in a plane?

There are three piles of stone with 3, 4, and 5 stones, respectively. Two players take turns removing any number of stones from a single pile. The player who takes the last stone wins. Which player has a winning strategy, and what is it?

Three points are chosen randomly on the circumference of a circle with radius 1. What is the probability that the triangle formed by the three points contains the center of the circle?