(don't tell Cashin we're doing math...)

In phase 1, you put a marble in boxes 1, 2, 3, 4, ...,1000 (so in all of them).

In phase 2, you put a marble in boxes 2, 4, 6, 8, ..., 1000.

In phase 3, you put a marble in boxes 3, 6, 9, 12, ..., 999.

And so on. In the last 500 phases, you just put a single marble in boxes 501 to 1000.

The following questions apply to the situation after all 1000 phases are completed:

1. Which box(es) have exactly 1 marble?

2. Which box(es) have exactly 2 marbles?

3. Which box(es) have an odd number of marbles?

4. What does the number of marbles really represent in relation to the number of the box?

For questions 1-3, you don't need to list all the boxes with a specific number of marbles, just identify some common property they have.

]]>Both circles here are the same size. Calculate their radius.

]]>Also, what happens if it's lowered by 1% 10000 times first, and then raised by 1% 10000 times?

(For the purposes of this problem, you should assume that a price can have any precision, so don't round them to 1/100 of a bit, or anything like that. Only the final result should be rounded.)

@StrawberryMilk Simp Before you ask: Yes, I realize that this problem is totally ridiculous and unrealistic

]]>You have a 3-gallon container, and a 5-gallon container. You have access to a source of water and a sink. Your goal is to have exactly 4 gallons of water in the 5-galloon container. How can you do that?

]]>Spoiler

Q: How to post in the Thoughts section?

A: You need to have club moderator rights to do it, contact me and I'll grant them to you.

Any questions or suggestions about the club go here.

]]>@Thankful Brony 42 2 points

@arashi_ 1 point

@Astralshy 0.5 points

]]>It's a well-known fact (and easy to prove) that all square roots of non-square natural numbers are irrational. But knowing that, can you prove that the sum of any two such square roots is also irrational?

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