(Just A Fun Riddle) There are 1 million closed school lockers in a row, labeled 1 through 1,000,000. You first go through and flip every locker open. Then you go through and flip every other locker (locker 2, 4, 6, etc...). When you're done, all the even-numbered lockers are closed.

You then go through and flip every third locker (3, 6, 9, etc...). "Flipping" mean you open it if it's closed, and close it if it's open. For example, as you go through this time, you close locker 3 (because it was still open after the previous run through), but you open locker 6, since you had closed it in the previous run through.

Then you go through and flip every fourth locker (4, 8, 12, etc...), then every fifth locker (5, 10, 15, etc...), then every sixth locker (6, 12, 18, etc...) and so on.

At the end, you're going through and flipping every 999,998th locker (which is just locker 999,998), then every 999,999th locker (which is just locker 999,999), and finally, every 1,000,000th locker (which is just locker 1,000,000).

At the end of this, is locker 1,000,000 open or closed​

Locker 1,000,000 will be open.

Explanation:

If you think about it, the number of times that each locker is flipped is equal to the number of factors it has. For example, locker 12 has factors 1, 2, 3, 4, 6, and 12, and will thus be flipped 6 times (it will end be flipped when you flip every one, every 2nd, every 3rd, every 4th, every 6th, and every 12th locker). It will end up closed, since flipping an even number of times will return it to its starting position. You can see that if a locker number has an even number of factors, it will end up closed. If it has an odd number of factors, it will end up open.

As it turns out, the only types of numbers that have an odd number of factors are squares. This is because factors come in pairs, and for squares, one of those pairs is the square root, which is duplicated and thus doesn't count twice as a factor. For example, 12's factors are 1 x 12, 2 x 6, and 3 x 4 (6 total factors). On the other hand, 16's factors are 1 x 16, 2 x 8, and 4 x 4 (5 total factors).

So lockers 1, 4, 9, 16, 25, etc... will all be open. Since 1,000,000 is a square number (1000 x 1000), it will be open as well.

Brainliest?

98 points!

assignment

analyzing characters

respond to the following questions in one paragraph for each. use specific examples from the text to support your responses.

1. there is a set of twins on the island named sam and eric. however, when describing them, golding regularly refers to them as samneric. how does this way of describing the twins relate to their behavior and the way that readers understand their characters? what examples of their behavior readers see that samneric is really the appropriate way to refer to them?

2. as the boys set out to search for the beast, ralph allows jack to lead the way, and he sinks to the back of the pack, " to have escaped responsibility for a time." what does this moment lead you to infer about ralph and about his feelings about being the group’s leader? what does this moment foreshadow?

3. while part of the party searching for the beast, simon realizes that the notion of the beast that the other boys have does not make sense. a beast sitting atop a mountain with claws, a beast who did not leave tracks, could have easily caught the twins. simon has a different picture of the beast: "there rose before his inward sight the picture of a human at once heroic and sick." how does this picture relate to the beast that samneric saw? how does it relate to what simon said earlier about the beast being "only us"?

no plagarism

me

no se

explanation:

no se