## Issue 4 – Apr 2023

### Quilt

Henry Ernest Dudeney – 1919A 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?

### Unique To Sum

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?

### Max Regions

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

### Nim

Charles L. Bouton – 1901There 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?

### Circle Center

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?