There are two gears interlocking as shown in the picture. Given that the large one has 16 teeth and the small one has 12 teeth. When the large gear makes three complete rotations, how many rotations does the small gear make?

Let's observe Figure 1 and determine: when Gear A is about to make one complete turn, among positions a, b, c, d and e, which one does tooth 'x' move to (in Figure 2)?

Four gears are numbered and arranged as shown in the picture. The first one has 40 teeth, the second one has 20 teeth, the third one 80 teeth and the fourth one has 10 teeth. When Gear 1 makes one complete rotation, how many rotations does the fourth one make?

John wants to color the shape below. Given that adjacent circles will be painted differently. How many colors at least does he need?

Mie colors an umbrella with 16 sections by 4 different colors: blue, red, purple and yellow. Given that each section will be colored by one color and all colors have to be used. Adjacent sections are colored differently. What is the most time she can use red color?

Lan has 4 crayons in different colors. She wants to color 3 countries in a map differently. Given that two countries sharing the same border are colored differently. How many ways can she color the map?

What does the word "Gear" mean?

What does the word "Interlocking" mean?

What does the word "Teeth" refer to in a mechanical context?