Math Is Fun Forum

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.

Edit 28/9/2024: I didn't feel right about posting code, so I've now deleted them.

I coded it up in LibertyBASIC.

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.

I solved it in M, using my BASIC strategy which was my first solution method.

Then I also worked out a not-too-tedious Excel solution.

Solved it in Excel, then with Mathematica.

And, just to keep my hand in with BASIC, solved it using Liberty BASIC (used the Sieve of Eratosthenes).

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.

Hi Keep_Relentless;

Sorry...I wasn't thinking and replied in the 1-3 thread instead of here. So here's what we said over there:

And you had much more fun!

I went the LCM route...

Also solved it in M later.

Hi Bob;

Is the "third number" that you're referring to 13195?

If so, its prime factors are the "5, 7, 13 and 29" from Keep_Relentless's post: ie, 5 x 7 x 13 x 29 = 13195.

...or am I missing something there?

Hi Bob;

When I'm logged in I get this:

And when I'm logged out I get this:

I get the same effect on the 'LaTeX - A Crash Course' pages here and here.

As there's no mention in the LaTeX thread back then of there being black text on black background, I suspect that the problem is newish.

Inspired by the second image in my post #52, my theory was that for both X1 & Y1 >17 digits, there'd be 'solutions' if their lengths are equal and their first 17 digits are equal (or nearly equal). However:
   1. My first trial, with X1 & Y1 both 24 digits long & the first 18 digits equal, resulted in the 'solution' as per the image below...which yielded the coveted "WOW!".
   2. My next trial, with X1 & Y1 both 30 digits long, resulted in no 'solutions' (tried equal digits from first 15 to first 30, all in vain). Hmm...

Conclusion: There are many, many 'solutions', but I haven't found the 'rule' that discovers them all.

As you can see, X1 & Y1 differ by 999,999. There would be many 'solutions' in that X1:Y1 range.