How it works
- There are 30 lights in a row, numbered 1 to 30. They all start off.
- There are also 30 students, numbered 1 to 30. They take turns one at a time, in order: Student 1, then Student 2, then Student 3, and so on.
- On your turn, start at the light with your own number, then count by your number. Flip every light you land on, and walk past all the others without touching them.
- Flip means switch it: an off light turns on, and an on light turns off.
| Student | Starts at | Counts by | Flips these lights |
|---|---|---|---|
| 1 | light 1 | 1s | 1, 2, 3, 4, 5, … (every light) |
| 2 | light 2 | 2s | 2, 4, 6, 8, 10, … (not light 1!) |
| 3 | light 3 | 3s | 3, 6, 9, 12, 15, … |
| 20 | light 20 | 20s | only light 20, because 40 is past the end of the row |
When every student has had a turn, which lights are on?
Questions people often ask
- Does Student 2 start at light 1?
- No. Every student starts at the light with their own number. Student 2’s first light is light 2, then 4, 6, 8, and so on.
- What if a light is already on?
- Then flipping it turns it off. A light can go on, off, on, off… many times during the game.
- Does a student flip a light more than once?
- No. Each student flips each of their lights exactly once, walking from the start of the row to the end.
- What happens to the lights a student skips?
- Nothing. They stay exactly as they were.
- How many students are there?
- The same as the number of lights. The last student, Student 30, flips just one light: light 30.
- Why do the later students flip so few lights?
- When you count by a big number, you run past the end of the row quickly. Every student after Student 15 flips only their own light.
- In “Guess first”, what does “on afterwards” mean?
- After this one student’s turn, not after the whole game.