Puzzle Prime Column

1. Insight

Draw 2 squares in the schoolyard in order to separate all students from each other.

The solution is shown below.

2. Riddle

What is 3/7 CHICKEN, 2/3 CAT, and 1/2 GOAT?

The answer is CHI + CA + GO = CHICAGO.

3. Deduction

Draw a continuous non-intersecting fence that separates the wolves from the sheep. The numbers on the signs indicate how many fence segments there are around the corresponding cells.

The solution is shown below.

4. Lateral

Somehow, you end up in a room that has three doors. Behind the first door, there is a deadly poisonous gas. Behind the second door, there are trained assassins with knives. Behind the third door, there are lions that have not eaten in years. Which door would you choose to open?

You should open the door with the lions. If they have not eaten in years, they will be dead already.

5. Math

You have 100 blue and 100 red points in the plane, no three of which lie on one line. Prove that you can connect all points in pairs of different colors so that no two segments intersect each other.

Connect the points in pairs of different colors so that the total length of all segments is minimal. If any two segments intersect, you can swap the two pairs among these four points and get a smaller total length.