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#676 2013-10-06 11:43:50

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Add 99 more and post it forever.

66924

66 + 9 + 24 I think that idea works every time too.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#677 2013-10-06 12:31:34

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

Re: Add 99 more and post it forever.

No...only sometimes.

67023

FromDigits[Reverse[{6, 7}]] + 0 + 23=99

Looks like for any number abcde, FromDigits[Reverse[{a, b}]] + c + de=99

Last edited by phrontister (2013-10-06 12:41:58)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#678 2013-10-06 12:42:33

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Add 99 more and post it forever.

Do you have one where it does not?

2 x 15^3 + 19^3 + 26^3 + 33^3 = 67122

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#679 2013-10-06 13:01:25

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

Re: Add 99 more and post it forever.

Yes...eg, 15741, 42372, 99990. In fact, that approach (which is formula 5 below) gives only 81 solutions out of 909 possibles, while the other formulas give more.

I listed all 909 five-digit multiples of 99 and tested 5 formulas to see how many solutions I'd find. Here are the results:

Using 'abcde' for the 5-digit multiples...
1. a+bc+de=99: 855 solutions
2. FromDigits[Reverse[{a,b}]]+c+de=99: 855 solutions
3. ab+c+FromDigits[Reverse[{d,e}]]=99: 90 solutions
4. ab+cd+e=99: 90 solutions
5. ab+c+de=99: 81 solutions

- Formulas 1 & 2 gave the same results for each test number.
- Only 54 numbers didn't sum to 99 with any of these formulas. Instead, they summed to 198 (2x99): all with formulas 1 & 2, 1 with formulas 3 & 4 and 10 with formula 5.
- Formulas 3 & 4 gave the same results for only 10 test numbers, with all of them being in the 90090 to 99000 range.

Conclusion: Using N = a 5-digit multiple of 99, T = a multiple of 10000, and M = 99's multiplier, formulas 1 & 2 work for all N<T where M>0.01T.

------------------------------------------------------------------------------------------------------------
67221

FromDigits[Reverse[{6,7}]]+(2+2)!-1=99

Last edited by phrontister (2013-10-07 02:50:34)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#680 2013-10-06 22:56:43

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Add 99 more and post it forever.

Hi;

Thanks for the work!

16^3+20^3+22^3+26^3+30^3=67320

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#681 2013-10-07 03:52:43

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

Re: Add 99 more and post it forever.

Thanks! It was a nice way to pass some spare time.

67419

n=Total[IntegerDigits[Total[IntegerDigits[67419]]]]; FromDigits[{n, n}]=99

Bedzzz!

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#682 2013-10-07 04:22:37

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Add 99 more and post it forever.

16^3 + 18^3+ 25^3 + 26^3 + 29^3 = 67518

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#683 2013-10-07 10:39:00

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

Re: Add 99 more and post it forever.

67617

n=DigitRoot[67617];FromDigits[{n, n}]=99

This pseudo code in M works for any correct entry in this thread just by substituting the multiple of 99 for mine.

Prediction: One day someone will come up with a DigitRoot command.

Last edited by phrontister (2013-10-07 11:37:26)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#684 2013-10-07 11:52:53

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Add 99 more and post it forever.

Hi;

What would you want DigitRoot[n] to spit out?

17^3+19^3+21^3+27^3+30^3=67716

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#685 2013-10-07 12:16:03

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

Re: Add 99 more and post it forever.

The single-digit end result of the iterative digital summing of n.

eg, n=67815=6+7+8+1+5=2+7=9...so I'd like DigitRoot[n]'s result to be 9.

There's some longish code on the net about it which I ignored for posting here and went for the pseudo code instead.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#686 2013-10-07 12:20:56

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

Re: Add 99 more and post it forever.

What's wrong with M's command?

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#687 2013-10-07 12:24:17

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Add 99 more and post it forever.

You want to use the command in your posts in the long form?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#688 2013-10-07 13:19:39

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

Re: Add 99 more and post it forever.

Hi Bobby,

No, just in a short form. Ideally, I'd like a one-word command for that, but it doesn't exist, does it? What is the shortest alternative you know of?

68013 (catchup)
68112

6+81+12=99

anonimnystefy wrote:

What's wrong with M's command?

I made 'DigitRoot' up. Do you know of a command that will do what I want? (see my previous post)

Last edited by phrontister (2013-10-07 13:25:52)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#689 2013-10-07 13:54:59

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Add 99 more and post it forever.

DigitRoot[n_] := If[Mod[n, 9] == 0, 9, Mod[n, 9]] silly but works.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#690 2013-10-07 21:22:23

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

Re: Add 99 more and post it forever.

Thanks, Bobby! That works well.

However, I've tried in my posts to avoid using numbers other than 99 and the post's answer - except for factors - and, inspired by your idea, I've now come up with this:

Mod[68310, 99] + 99 = 99

Last edited by phrontister (2013-10-07 22:24:06)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#691 2013-10-07 21:41:14

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Add 99 more and post it forever.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#692 2013-10-08 10:18:43

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

Re: Add 99 more and post it forever.

68508

68508/post#=99

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#693 2013-10-08 20:12:21

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Add 99 more and post it forever.

68607

6 + 86 + 0 + 7 = 99

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#694 2013-10-08 20:20:56

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

Re: Add 99 more and post it forever.

68706

Rotate[FromDigits[{6+87*0,6}],\[Pi]]=99

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#695 2013-10-08 20:23:19

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Add 99 more and post it forever.

68805

13^3+14^3+16^3+30^3+32^3=68805

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#696 2013-10-08 20:26:00

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

Re: Add 99 more and post it forever.

68904

6!/8+9+0x4=99

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#697 2013-10-08 20:49:31

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Add 99 more and post it forever.

16^3+2 24^3+26^3+27^3=69003

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#698 2013-10-08 21:09:27

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

Re: Add 99 more and post it forever.

69102

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#699 2013-10-08 21:13:36

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Add 99 more and post it forever.

15^3+20^3+2 21^3+34^3=69201

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#700 2013-10-08 21:18:02

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,594

Re: Add 99 more and post it forever.

69300

69+30+0=99

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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