# Brain Teaser (1) 腦筋急轉彎（一）

in #cn6 years ago

During my time at uni, I made friends with a lot of physicists and mathematicians. Most of us had a common feature: we like to think about interesting problems. I guess that's the primary reason why we could survive the degree! One of them went as follows:

Suppose we have 100 light bulbs, labelled as 1,2,3....,100. Each of them comes with an on/off button so that if it's on and we press the button, it turns off and vice verse. Initially, all these light bulbs are off. Now, we press the buttons of those that are labelled by a multiple of 1. The result is that all the light bulbs are now on, because all integers are multiples of 1. Next, we press those that are labelled by a multiple of 2. Then, all the even-numbered ones are off and all the odd-numbered ones are on. We repeat this for multiples of 3, multiples of 4, etc, up to multiples of 100. The question is: Which light bulbs remain on in the end?

For those who can program, this problem is easily solved computationally, but that will not be fun because you won't have to do any thinking. If you insist to solve it computationally, change the number from 100 to 100 million million to make it more challenging!

Sort:

6 years ago (edited)

1×8
2×4
4×2
8×1

1×9
3×3
9×1

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