Math Is Fun Forum

...or three!!

Hmmm...that's odd! OneDrive has always worked for me before.

Try these links. They're on Filedropper, which I've never used before. It works when I tested it, but you have to complete a captcha for each file...which I didn't know before I uploaded them.  

Number
Solution

What file host do you use for file sharing on forums?

Edit: The above links no longer seem to work, so I went back to post #33 and changed the links to ones that work...at least for now (for me)!

It's the same idea as my post #19, where I included it in the first line of your code that I changed.

This time I made it a bit bigger...and I'm not sure if I should try it on your code!

Maybe you're a rough diamond?

His code backs that up!.

I tried his and George's codes on a random 100,000-digit number that has a solution. JM's took approx 14.3 seconds to solve it, and George's approx 767 seconds. So their speed comparison has changed dramatically with this much larger number!

Hi Bobby;

'Obsolete'?? I take it the meaning is in the teenage-speak word-inversion sense.

As wicked = good/great, and sick = cool/awesome, so obsolete = now/happening/up-to-the-minute. eg, someone referred to as being 'obsolete' is really a now (as in right now)/up-to-date person, with his finger right on the pulse. And no, he's not checking his pulse to see if it's still ticking!

Just to confirm that it's not the number size that's the problem with your code, I gave it this 1000-digit number to solve:

I don't know how long it took because I forgot to include the timer in the code, but it started looking for the answer late this afternoon, was still busy at it 3 hours or so later when I had to go out, but when I got home 2-and-a-half hours later it was waiting for me with the answer:

JM found the same solution as yours in 0.004 seconds, and George found it in 0.020 seconds.

George's check says "True" in each case, but I haven't checked it myself. I'm happy to accept George's code's say-so!

I don't know what the number was, as I used RandomInteger[10^50] to generate it and didn't save it.

This is my changed version of your code that I used. It includes George's check.

m=RandomInteger[10^50]
n=IntegerLength[m];
var=Table[Subscript[a,k],{k,n,1,-1}];
f=Sum[1/9 (-1+10^k) Subscript[a,k],{k,1,n}]==m;
s=FindInstance[Append[{f,10>Subscript[a,1]>0},Table[10>Subscript[a,k]>=0,{k,2,n}]]//Flatten,var,Integers];
FromDigits[Flatten[var/.s]]
Total@NestWhileList[Floor[#/10]&,%,#>0&]==m

I think you'll find most numbers will work: eg, 69586679352243945460884074620809492862023430738549. That works in JM's & George's too, and comes up as "True" in George's check.

38994141682523903136734583674252327906171348631335 has a solution, but your code complains. Try it!

Interesting...what I understand of it!

Anyway, here are some things I've noticed:

1. A correctness check is needed, as george2079 said.
   eg, 12398 and 123476 have no solution, treated this way by the 3 codes:
    - george2079's code gives "the 'closest' value", and, helpfully, his check announces "False";
    - J. M.'s code just gives the 'closest' (I suppose) value - like george2079 - with no correctness announcement;
    - Your code gives strange-looking answers...which probably indicates that they don't have a solution.

2. george2079's code has an error that prevents me from running his program (one of the closing brackets after Divide @@ # has to go), and should be:

m = 308460277;
Reap[NestWhile[{#[[1]] - #[[2]] Sow@Floor[Divide @@ #], 
      Floor[#[[2]]/10]} &, {m, 
     FromDigits@ConstantArray[1, Ceiling@Log[10, m]]} , #[[2]] > 
      0 &]][[2, 1]] // FromDigits

3. george2079's check could be improved by replacing the answer input with "%", like so (his way would have been for clarity's sake, I guess):

Total@NestWhileList[ Floor[#/10] &, %, # > 0 &]==m

4. Your code fails on some valid inputs (answers found by the other two guys' codes): eg, 12333, 12344, 12355, 12366, 12377, 12388, 12399.
    They might be the only fails, but I didn't check right up to infinity.

5. A little tweak for your code (which I know you already know! )

First line: m = 308460277; n = IntegerLength[m];

I wonder what percentage of numbers fail, and their composition? But I don't really need to know...

Hi Bobby;

I tried to code it in M, but only succeeded with the BASIC approach like in my post #6 (but with slightly shorter code):

aa={A,G,P,W};
ff={F,P};
bb={B,T,Z};
ee={E,M,Q,R};
For[a=1,a<5,a++,For[f=1,f<3,f++,For[b=1,b<4,b++,For[e=1,e<5,e++,
Print[aa[[a]],ff[[f]],bb[[b]],ee[[e]]]]]]]

Anyway, something new I learned was that uppercase E (in variable ee) is reserved for exponential constant e.

At first I thought I'd have to change the letter, but then discovered that although M's output prints E as e, when the output is copied as plain text and pasted here (and in other software), e prints as E.

Hi thickhead;

Looks like you left out the opening instruction about writing {B,T,Z} into Column C.

Works fine, otherwise.

Even so, my scratching implements are much shorter and blunter than yours. My time is taken up with so many other things that M will always have to take a back seat. Can't see that ever changing...

Do you mean the new ones in the recent new M version? I haven't upgraded...too costly and probably not needed for my junior use, I think.

It's been very interesting...thanks for starting us off!