There are one hundred lightbulbs all in a row. Each one starts turned off.

Someone flips the switch on every single lightbulb

Someone flips the switch on every other lightbulb

Someone flips the switch on every third lightbulb

Someone flips the switch on every fourth lightbulb

...

Someone flips the switch on every hundredth lightbulb

How many light bulbs are turned on?

Guest Nov 2, 2019

#1**0 **

Does the flipping only go to the 4th light bulb?

Or does he keep flipping until he flips all 100 lightbulbs?

CalculatorUser Nov 2, 2019

#2**0 **

Of course the flipping stops after the foruth bulb. It would be too dark to see anything if more were turnd off.

Guest Nov 2, 2019

#3**0 **

lol i had a solution ready, then deleted it because I thought it continued to 100. nuuuuuuuu

EDIT: I remade it,

below is the explanation

CalculatorUser
Nov 2, 2019

#4**+2 **

Use Binary sequences ( a sequence of ones and zeroes) to help visualize.

*Someone flips the switch on every single lightbulb*

Every lightbulb starts turned on. ON is 1, OFF is 0.

1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111

*Someone flips the switch on every other lightbulb Someone flips the switch on every third lightbulb Someone flips the switch on every fourth lightbulb*

This means that LCM of 2, 3, 4,. Which is 12.

A binary sequence of 12 terms would repeat in the a hundred light bulbs.

So lets have 12 light bulbs.

101010101010 *Someone flips the switch on every other lightbulb*

100011100011 *Someone flips the switch on every third lightbulb*

100111110010 *Someone flips the switch on every fourth lightbulb*

There are 7 out of 12 lightbulbs that are turned on.

Now we have a pattern of 100111110010 repeating until the number of terms is 100. We have to find the number of 1s in that 100-length pattern.

Every 12 terms that are seven 1s.

So 12 * 8 = 96

8 * 7 = 56

So out of 96 terms, 56 are 1s.

There are 4 more terms.

Counting up the pattern 100111110010 four terms, we have two 1s.

So 56 + 2 = 58

**58 light bulbs are turned on**

CalculatorUser Nov 3, 2019