Math Is Fun Forum

Problem 10 done on Mathematica.

Problem 11 could be done on Excel but I think it would take annoyingly long if I'm not missing something. I'm going to go ahead and guess that it's the diagonal 89 * 94 * 97 * 87.

Edit: Problem 12 done with Mathematica. Would be very surprised if it could be done with Excel.

Edit 2: Problem 11 done on Excel.

You have been busy!

I got problem 9 with a mixture of Mathematica and Excel. Is it considered cheating if you use Mathematica? You don't have to understand how the maths is done to use it. But you've got to start somewhere, it's useful incentive to learn to use Mathematica better. I will consider it as partial credit, haha, because I got formulas for a and c in terms of b and I have no idea how they were derived, but I was then able to hunt for answers systematically.

I will consider it full credit if you understand how the computer did it (or at least some theory that would let you arrive at the same conclusion), and partial credit otherwise. So I have labeled my excel for problem 9 "partial credit".

But by this criterion, we would be allowed to get the answer directly often, because there's often a simple iterative process. By this criterion, if I understand the sieve of eratosthenes, to cross out the multiples of every prime, I have a (laborious) method I could potentially carry out on pen and paper. So it is not really a mystery how the computer arrives at the answer.

I'm trying to justify myself in using M so we can go on to problems 10-12! I'll just go ahead and post them.

In case there's a way of explaining what M spit out regarding problem 9, I will share its result:

Good post Bob.

But I have some doubts that we can't say anything at all.

Can we generalise this to say there is no way of determining the probability of an event that violates the laws of nature?

It seems to me like the probability should be much higher if you believe the sources that claim miracles have happened (in connection with Jesus).

And much lower given that many experiments have been done in which the laws were not violated.

If you believe the Bible 100%, then the probability of a rapture occurring is 100%. The only question is when.

If you don't believe the Bible 100%, then I would expect the probability of a rapture to be getting lower with every day that passes without a rapture, and every day that passes with no independent confirmation of miracles.

Am I over-surmising here?

K_R

I don't think it is as simple as Outcome / Possible Outcomes (at least not at the macro-level). Although it's good for die or roulette, that model assumes every outcome is equally likely. But through induction we can say that, in general, a miraculous event is much less likely than a natural one. So we have to weight the different outcomes differently. It's further complicated by the fact that there are an infinite number of events, miraculous or natural, that could take place given enough time/space (or arbitrarily small units of space/time).

Suppose we guess 0.001 (with three zeros) is the smallest number. We can find a smaller one: 0.0001 (with four zeros). And yet a smaller one: 0.00001 (with five zeros). This process can continue forever; there is no limit to the number of zeros we can add. So there is no smallest positive number.

My explanation is not as fancy as the others, but it works for me.

For part 2, I would do (9/21)*(12/20) + (12/21)*(9/20). That is, the probability of selecting first blue then green, plus the probability of selecting first green then blue.

It is 101/125, Europe just accidentally wrote 101/25.

K_R

Hi,

Yes looks right.

Not sure whether problems 7 or 9 can be done on Excel in a reasonable amount of time.

Wow, you just used a calculator for #5? I made columns checking divisibility by every number up to 20 and searched for a good while. Found 46512 is divisible by 16-19, checked its multiples. Found a multiple divisible by every number 1-20 except for 11. Found the smallest one that fits 11 too.

But it was not as quick and easy as using a calculator!

I don't really know what I'm doing, but I made it this far.

Edit: If you want, you can make an account on the website Project Euler which has hundreds of these problems, and a forum for each problem you can view after you complete it where people share their code etc. These are the easy problems copied directly from that site.