Light bulb switching brain teaser | Puzzles | Math for fun and glory | Khan Academy

TL;DR

After 100 passes, the light bulbs that will be on are the perfect squares between 1 and 100.

Transcript

Let's say we have 100 light bulbs. Well, let me actually just draw them. So I have one light bulb there. I have another light bulb. And I have 100 of them. 100 light bulbs. And what I'm going to do is-- Well actually, before I even start turning these light bulbs on and off, let me let you know that they are all off. So they start off. Now, the nex... Read More

Key Insights

• 💡 The brain teaser involves a series of passes where light bulbs are turned on and off.
• 💡 Light bulbs are switched based on their numbers being multiples of the pass number.
• 💡 Light bulbs with an odd number of factors will stay on after multiple passes.

Questions & Answers

Q: How many light bulbs are still on after 100 passes?

There are 10 light bulbs that will remain on after 100 passes. These are the perfect squares between 1 and 100.

Q: Which light bulbs will be on after 100 passes?

The light bulbs with the numbers 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 will be on after 100 passes. These are the perfect squares between 1 and 100.

Q: What is the pattern in the numbers of the light bulbs that stay on?

The light bulbs that stay on are always perfect squares. This is because perfect squares have an odd number of factors, making them the only ones to remain on after multiple passes.

Q: Is there a specific formula to determine the number of light bulbs that will stay on?

The number of light bulbs that will stay on can be found by counting the number of perfect squares between 1 and the maximum number, in this case 100. In this scenario, there are 10 perfect squares, so 10 light bulbs will stay on.

Summary & Key Takeaways

• The brain teaser involves a series of passes where light bulbs are turned on and off.

• Each pass switches specific light bulbs based on their numbers being multiples of the pass number.

• The light bulbs that remain on after 100 passes are the perfect squares between 1 and 100.