Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

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How about you write it down now, in this forum?

Yes. But maybe loaded, as in not fair.

In other words, show that

is not a product of and where for all i and**Agnishom**- Replies: 4

Show that you cannot have two loaded 6-faced die, such that, when you roll them together all scores from 2 to 12 are equally likely

Hi there;

Loosely speaking, an algorithm is a step by step recipe of solving a problem.

Algorithms in mathematics are ubiquitous. Can you calculate 123 + 23? Yes, you can do so because you learnt an algorithm to do so in primary school.

Algorithms are a lot of fun. An interesting (and very approachable) book on algorithms is "Algorithms Unlocked" by Thomas Cormen.

The computation.

I'd like to see your program.

That is very good! How much time did it take?

So far so good, but I am only playing around.

Do you like the weekly problems?

Now they do again. You wanted that, didn't you?

Brilliant.Org now has weekly problems

I know how to solve it for an 8 by 8 board.

I do not know how one does infinite similations.

In that case, I think the knight case is similar..

Oh, I hope that is fun!

Yes, let's solve a simpler problem first

I meant, what is the expected time after which you return to the origin in the following random walk?

Start at 0. When in i, with probability 0.5, go to i+1, and with probability 0.5 go to i-1

I can find this value for a finite n. But I do not think taking limit on n makes sense.

What is the mean time of return to the origin when you do a random walk on the integers?

**Agnishom**- Replies: 13

A knight on an unbounded chess board picks one of the possible 8 moves uniformly at random. What is the expected time after which the knight comes back to where it started?

Does a name start with a small letter?

That sounds interesting to me.

Keep going.

Have you heard of Princess Consuela Banana Hammock?

Oh okay, thank you.

Do you have other suggestions?

But this thread is about getting suggestions, so that he knows what is the best to name himself.

Einar is not an unique name. There are people named Einar. We are looking for unique names, like Agnishom. There was no one called Agnishom before me.

How do you pronounce Einar?

He wants to change his name.

Einar sounds like an interesting name. Do you have any more of these? Preferably something original

No, a real name for himself.

**Agnishom**- Replies: 15

Hi;

I have a friend who is looking for a new name for himself. He wants it to be an unique name.

Please suggest ideas.