Math Is Fun Forum

I've solved #48 in M...a bit too big for Excel!

Not too big for my freeware Just BASIC program, though.

That's how I first solved it in M, but later improved it to follow the more standard M way with their functions.

I looked for a method in M for half an hour or so, but formed no real idea on how to go about it.

So, I opened my trusty Excel, and found the answer in about 20 minutes.

I'll have to try M again, though...but not sure when.

From bobbym's signature: Always satisfy the Prime Directive of getting the right answer above all else.

PS...I found a solution in M, but need to work a bit on my code still.

Hi K_R;

I've done 16, 20 & 25, but that'll do me for now (bed time).

I used M for all three, with #25 taking the longest. For that one, I initially found a solution with a For loop, but then a better one with M's Fibonacci function, which I didn't know existed until it occurred to me that it might.

Hi again, Relentless! Still 'Keep_'-ing the old name going, I see.

Yes, I thought you were you, your username being a good clue; + your use the other day of 'M' for Mathematica, the abbreviation that bobbym and I used frequently in our many conversations...and maybe you did in yours with him too.

We met in several threads about 8 years ago, one being The missing dollar (& the 2 extra dollars). Well, the sad news since then is that my HP 32SII that I based the puzzle on conked out 3 years ago. However, I found an HP 33S (HP 32SII's successor) for only $35, and all's happy again.

Welcome back!

I couldn't think of an easy enough way in Excel, so went with M:

I'd overlooked what you said there. I haven't posted any answers as such, just code...but running the codes will give the answers.

Shall I continue posting the way I have, or change somehow?

From their website:
"Who are the problems aimed at?
The intended audience include students for whom the basic curriculum is not feeding their hunger to learn, adults whose background was not primarily mathematics but had an interest in things mathematical, and professionals who want to keep their problem solving and mathematics on the cutting edge."

I fit into the italicised category.

I coded it up in LibertyBASIC (it'll run in the freeware Just BASIC too):

No clever maths, just loops...which is all I can manage this time of night!

Yes, I'd also be very surprised, given the huge numbers. But maybe an Excel whizz could...

I also solved it with M.

Verified the solution in Excel via a UDF that gave all the divisors, and a formula that counted the number of divisors. Both helps were found on the net. Also, I needed the triangular number from the M solution because of the huge numbers.

Your 500(2-√2)<b<500 is close to what I did, but I don't understand the other two. Sorry.

But here's how I solved it in M:

I didn't reinvent the wheel there...just used my BASIC strategy, which was my first solution method.

And here's my BASIC code:

Coded in Liberty BASIC, but also runs in Just BASIC (junior freeware version of LB).

I also worked out a not-too-tedious Excel solution (it looks more laborious than it is):   

I hope those Excel instructions work for you!

The Excel solution I mentioned in post #5 is a single column one that lists all the primes to the 10001st.

Mathematica has a 1-word function for returning just the 10001st prime.

My Liberty BASIC program came with a 'Sieve of Eratosthenes' module, which I adapted (clunkily) to return these options:
   (a) just the 10001st prime, or
   (b) all primes up to and including the 10001st.

Hi Keep_Relentless;

I did #7 on Excel spreadsheet, but, after failing to come up with anything myself, cheated by using a UDF I found on the net that helped (but I won't reveal what/how, yet).