Moving on to a Maths Puzzle

[thetank]

But like in craps, the probability of very small numbers and very big numbers being rolled will be symmetrical and very neatly cancel each other out.

Unlike in craps, the small number begins at zero. Easy when you know the answers.



Here's my favourite from that site.....

Q - Find the smallest natural number greater than 1 billion (10⁹) that has exactly 1000 positive divisors.  (The term divisor includes 1 and the number itself.  So, for example, 9 has three positive divisors.)

A - Of course, it is 1,060,290,000.


That guy should really write trivia for christmas crackers

[Moskvich]

I don't think they're equally likely, there is only one way to make zero and a loads and loads, to use a techincal term, to make 182.

Presumably that doesn't matter, as the distribution of scores will be a normal curve around the 182-point, no..? So the 182s will be balanced out by 181s, 183s etc, which aren't divisble by 13.

Isn't the problem with this that there's a chance of getting 0. So there are 365 possible scores, not 364. Playing to 13, there's a 1 in 4503599627370496 chance of getting 0. (I just did it, but the floor's a right mess now).

So actually the chance of the score being divisible by 13 is marginally less than 1 in 13. But the discrepancy will be higher the lower down you go. Do it with just one ace - the chance of the score being divisble by 1 isn't 1 in 1, cos now there's a 50% chance of the score being 0.

[Moskvich]

But like in craps, the probability of very small numbers and very big numbers being rolled will be symmetrical and very neatly cancel each other out.

That's what I was saying too, only slower.

[AndrewT]

Correct my thinking if I'm wrong,

It would appear you all have.

So, given that they both give the same answer, is the correlation between the two answers merely a result of the fact that the top score is divisible by the required number, and that the unlikely scores either side of the centre cancel each other out?

Would the probability of the answer being exactly divisible by, say, 9, be far away from 1/9?

[thetank]

Book answer :   0.0769230769230802025049342773854732513427734375
Moskvich 1/13   0.076923076923076923076923076923077 (to a finite number of decimal places)

So aswell as being right, it looks like he's right about being wrong too.

What a guy 

[boldie]

Book answer :   0.0769230769230802025049342773854732513427734375
Moskvich 1/13   0.076923076923076923076923076923077 (to a finite number of decimal places)

So it looks like he's right about being wrong too.

yeah...way off the mark lol

[ifm]

He worked it out in less than one minute...fold 

Before i read the rest of the thread i just have to say LOL @ this.