sum of digit

anonimnystefy · 2012-05-05 22:48:05

I think gAr is summing all digits in the ones place then in the tens place and so on.

Without repetiton is neccesary because if it wasn't mentioned you could have the numbers like d1,d1d1,and so on,included too,which would be an infinite amount of numbers by itself. Not to mention if we brought in d2.

Also,I am seeing right now that gAr's aasumption might be wrong,and that it is not only n-digit numbers that need to be summed.

phrontister · 2012-05-05 23:09:22

Hi stefy,

Yes, I see now why "without repetition" was included. Thanks.

I think we need juantheron to clear this up, and maybe to give us an example.

bobbym · 2012-05-05 23:16:09

Hi phrontister;

When I first looked at the problem I had a whole different idea about it too. But after seeing gAr's solution I tend to think he is correct in how he is interpreting it.

anonimnystefy · 2012-05-05 23:19:52

I think we should all wait for juan to explain.

phrontister · 2012-05-05 23:21:57

Ah! Light dawns!! Yes...I go with gAr's interpretation too as to what juantheron is after.

Thanks, Bobby.

bobbym · 2012-05-05 23:22:53

An explanation from juan would remove any doubt.

phrontister · 2012-05-06 13:08:11

Hi Bobby,

Looks like when summing M's Permutation results this way, numbers with leading zeros are seen as valid (even though the zero isn't and gets dropped), which, if you used M, would be at least one reason why my answer for 10 differs from yours as I omitted such numbers in my LB program.

So the sum of the permutations of 306 in M is 1998, but in mine is 1899 because I treated 36 and 63 as invalid. But my treatment may be incorrect.

Re your answer 22175999997782400 for 10 in post #18. I got a different answer, but maybe my code is wrong:

I thought that the code would pick up all the permutations for numbers with digits 0 to 9, including numbers with a leading zero, because I'm using the same code as for 'My M' above, which gave the correct result.

Last edited by phrontister (2012-05-07 10:31:22)

bobbym · 2012-05-06 17:02:40

Hi phrontister;

FromDigits will not treat a leading zero as a legitimate digit:

FromDigits[{0,1,2,3}] returns 123 a 3 digit number.

I got a different answer,

Your answer for 0,1,2,3,4,5,6,7,8,9 is correct.

For a special reason so is mine. gAr's formula holds for special cases too. Supposing we had a number system 1,2,3,4,5,6,7,8,9,A where A had a value of 10 but was a single digit. Makes me dizzy just thinking about it. Sort of like Hexadecimal. That is what my answer is for.

By the way that is very impressive what you did with M there. You understand mapping, Total and a few other commands. Excellent!

phrontister · 2012-05-07 01:31:47

Hi Bobby,

Yes, learning a few things here and there...as the need arises from puzzles that I want to try in M.

Had my head down in the help files for quite some time before I worked this one out.

bobbym · 2012-05-07 01:34:16

If you understand that much then I would say you have everything you need.

phrontister · 2012-05-07 04:32:54

Hi Bobby,

I'm on the way...'on a slow boat to China'. Muuuch to learn yet, as the little people would say.

But my treatment may be incorrect.

I just downloaded a nice (for BASIC) permutations program from an LB forum. It gives the same result as M, and leading zeros print in the output (as do M's before FromDigits removes them).

I altered the program to ask for the initial number string and to display the sum of the string's permutations.

Unfortunately it only handles numbers below 9 digits long. The program shuts down after that due to low memory...probably because of dimming all permutations.

Last edited by phrontister (2012-05-07 10:34:32)

anonimnystefy · 2012-05-07 04:38:07

Arghhhh...you guys are such good programmers. I wish I could be somewhat better at programming.

bobbym · 2012-05-07 05:46:37

I'm on the way...'on a slow boat to China'.

Those boats sure are slow.

anonimnystefy · 2012-05-07 06:05:37

Hi m

What programming languages did you say you know?

bobbym · 2012-05-07 06:06:21

You mean which ones I forgot.

anonimnystefy · 2012-05-07 06:08:40

Proceed.

bobbym · 2012-05-07 06:18:53

At one time Forth, 3 or 4 Basics of course, Lisp, 2 or 3 Assembly languages, C++ and a smattering of others.

anonimnystefy · 2012-05-07 07:36:27

Have you ever heard of the pl called Brainf*ck? It uses only 8 symbols for its syntax.

bobbym · 2012-05-07 08:20:55

Yes, I thought is was just an oddity.

anonimnystefy · 2012-05-07 08:23:36

There is an eben stranger one. It is called Whitespace. I would like to get a compiler for it,but cannot manage to install one properly.

bobbym · 2012-05-07 08:29:36

Why do you want one?

anonimnystefy · 2012-05-07 08:35:27

I think it would be fun to program in Whitespace.

bobbym · 2012-05-07 08:40:19

Yes, but is it useful? Can you do anything with it that justifies the time spent?

phrontister · 2012-05-07 22:19:29

Hi Bobby,

Learnt a bit more M tonight. I used Select to enable me to sum just the numbers without a leading zero, which for 0,1,2,3,4,5,6,7,8,9 totalled 17942399998387200.

Happily ( ) , that is the same answer I got back in post #19, which is something I wanted to test as a proof for the correctness of the formula I came up with back then.

Select took a while to unearth. Before that I'd tried Cases (with Except and some patterns), Delete and some others I've now forgotten, but I couldn't get anything to work. Other functions will probably work somehow, but I tried lots of options and couldn't find the 'somehow' until Select.

bobbym · 2012-05-07 22:24:16

Hi phrontister;

Very good! You learned a little bit of the lambda calculus.

Math Is Fun Forum

#26 2012-05-05 22:48:05

Re: sum of digit

#27 2012-05-05 23:09:22

Re: sum of digit

#28 2012-05-05 23:16:09

Re: sum of digit

#29 2012-05-05 23:19:52

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#30 2012-05-05 23:21:57

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#31 2012-05-05 23:22:53

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#32 2012-05-06 13:08:11

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#33 2012-05-06 17:02:40

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#34 2012-05-07 01:31:47

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