[araver]

In a future not so far way, Earth archaeologists find on a far away planet a fragment from a long lost civilization.

This fragment involves an unknown operation *|*.

Unlocking its secrets may lead to a breakthrough in understanding their civilization.

Can you do it?

If

21 *|* 7 = 11

and

17924 *|* 10751 = 851

then how much is:

1982 *|* 2010 = ?

[araver]

Declaring open-season on questions again

Ask for a particular "a *|* b =?" and I'll oblige. (Of course, not the pair the OP asks for )

A recap on what was so far (including a question from amateur that I missed, sorry) :

 21 *|* 7 = 11

 17924 *|* 10751 = 851

 1089 *|* 121 = 2069

 10 *|* 23 = 6

 1 *|* 0 = 2

 999 *|* 909 = 1359

 14 *|* 14 = 14

 2 *|* 1 = 0

 1 *|* 1 = 1

and

a *|* b = b *|* a

Edited November 25, 2010 by araver

[araver]

Adding another hint to the list:

 21 *|* 7 = 11

 17924 *|* 10751 = 851

 1089 *|* 121 = 2069

 10 *|* 23 = 6

 1 *|* 0 = 2

 999 *|* 909 = 1359

 14 *|* 14 = 14

 2 *|* 1 = 0

 1 *|* 1 = 1

 a *|* b = b *|* a

 a *|* a = a

[Guest]

3 *|* 0?

[araver]

Adding it to the list

 21 *|* 7 = 11

 17924 *|* 10751 = 851

 1089 *|* 121 = 2069

 10 *|* 23 = 6

 1 *|* 0 = 2

 999 *|* 909 = 1359

 14 *|* 14 = 14

 2 *|* 1 = 0

 1 *|* 1 = 1

 a *|* b = b *|* a

 a *|* a = a

 3 *|* 0 = 6

[araver]

Unsure if anyone is still following this, but here's today addition to the list of clues:

 21 *|* 7 = 11

 17924 *|* 10751 = 851

 1089 *|* 121 = 2069

 10 *|* 23 = 6

 1 *|* 0 = 2

 999 *|* 909 = 1359

 14 *|* 14 = 14

 2 *|* 1 = 0

 1 *|* 1 = 1

 a *|* b = b *|* a

 a *|* a = a

 3 *|* 0 = 6

 13 *|* 8 = 18

[Guest]

A large number with a small number please? Let's say 17924 *|* 5.

[araver]

A large number with a small number please? Let's say 17924 *|* 5.

Certainly:

 21 *|* 7 = 11

 17924 *|* 10751 = 851

 1089 *|* 121 = 2069

 10 *|* 23 = 6

 1 *|* 0 = 2

 999 *|* 909 = 1359

 14 *|* 14 = 14

 2 *|* 1 = 0

 1 *|* 1 = 1

 a *|* b = b *|* a

 a *|* a = a

 3 *|* 0 = 6

 13 *|* 8 = 18

 17924 *|* 5 = 9329

[Guest]

Is a *|* 0 = 2*a?

[araver]

Is a *|* 0 = 2*a?

Not really, although in some cases it does. I'll add an example where it doesn't to the list.

 21 *|* 7 = 11

 17924 *|* 10751 = 851

 1089 *|* 121 = 2069

 10 *|* 23 = 6

 1 *|* 0 = 2

 999 *|* 909 = 1359

 14 *|* 14 = 14

 2 *|* 1 = 0

 1 *|* 1 = 1

 a *|* b = b *|* a

 a *|* a = a

 3 *|* 0 = 6

 13 *|* 8 = 18

 17924 *|* 5 = 9329

 16 *|* 0 = 23

[Molly Mae]

I'm intrigued...

1234 *|* 49

19 *|* 1

How long would it take you to calculate the above two operations individually? And do you use any type of calculator? Paper? Or is it all in your head?

[araver]

I'm intrigued...

1234 *|* 49

19 *|* 1

How long would it take you to calculate the above two operations individually? And do you use any type of calculator? Paper? Or is it all in your head?

1234 *|* 49=1780

19 *|* 1=10

And to answer your question: Well it takes a while cause it's not something you're accustomed to do. As I said it is alien. Aliens would probably take much less time.

I like to do it on paper just to be sure of the results, not to post a false answer. But I like to check it with a computer too (again, same reason).

I think it can be done in the head, at least for a small number of digits. For a large number even addition is hard, right?

Edited December 1, 2010 by araver

[Guest]

I've been looking at this for a while. I'm still not seeing the overarching pattern, but is the following true?

If a *|* b = c, then a *|* c = b and b *|* c = a.

Also, what are:

1 *|* 9

2 *|* 9

[k-man]

Are these numbers in base 10?

I don't suppose that the aliens were using our representation of the digits even if they used a decimal system. So, is it fair to assume that all the numbers in the examples are decimal representation of the numbers?

[araver]

I've been looking at this for a while. I'm still not seeing the overarching pattern, but is the following true?

If a *|* b = c, then a *|* c = b and b *|* c = a.

Also, what are:

1 *|* 9

2 *|* 9

Basically yes!

The rest:

1 *|* 9 = 20

2 *|* 9 = 19

Are these numbers in base 10?

I don't suppose that the aliens were using our representation of the digits even if they used a decimal system. So, is it fair to assume that all the numbers in the examples are decimal representation of the numbers?

Indeed, they might not and the OP doesn't specify it, so it is a justified question.

I would advise you to treat the numbers in the examples as their normal decimal representation. Suppose the explorers figured out the numbering system first and you're looking at the translation to our familiar decimal representation.

Edited December 1, 2010 by araver

[k-man]

1982 *|* 2010 = 16

The aliens had the numbering system with the base 3, so they only had digits 0, 1 and 2. Operation *|* is performed on each corresponding digit of a number in the following manner - if the 2 digits are the same then the result is the same (e.g. 0 *|* 0 = 0, 1 *|* 1 = 1, 2 *|* 2 = 2). If the digits are different, the the result is the 3rd remaining digit (e.g. 0 *|* 1 = 2, 1 *|* 2 = 0, 0 *|* 2 = 1). To compute the result for any 2 numbers first convert the numbers to base 3 representation and then apply the operation digit-by-digit. For example,

    012001

*|* 012122

    ------

    012210

[Molly Mae]

Very nice.

I should have seen that with 0 *|* 2 = 1...

I've been way off my game lately. I should stop knitting...

[araver]

1982 *|* 2010 = 16

The aliens had the numbering system with the base 3, so they only had digits 0, 1 and 2. Operation *|* is performed on each corresponding digit of a number in the following manner - if the 2 digits are the same then the result is the same (e.g. 0 *|* 0 = 0, 1 *|* 1 = 1, 2 *|* 2 = 2). If the digits are different, the the result is the 3rd remaining digit (e.g. 0 *|* 1 = 2, 1 *|* 2 = 0, 0 *|* 2 = 1). To compute the result for any 2 numbers first convert the numbers to base 3 representation and then apply the operation digit-by-digit. For example,

    012001

*|* 012122

    ------

    012210

It is nice, but the result of the operation 1982 *|* 2010 is not the one you claim.

[Guest]

Good job k-man! I was on my way there, but it would've taken me a lot longer to make the connection...

However, I think you dropped a couple digits you shouldn't have:

1960

I think I got that right...

[k-man]

Was in the rush to post it before somebody else does and messed up

1982 *|* 2010 = 1960

Here are all the given clues and the result converted to the base-3 system.

21	*|*	7	=	11				0000000210	*|*	0000000021	=	0000000102

17924	*|*	10751	=	851				0220120212	*|*	0112202012	=	0001011112

1089	*|*	121	=	2069				0001111100	*|*	0000011111	=	0002211122

10	*|*	23	=	6				0000000101	*|*	0000000212	=	0000000020

1	*|*	0	=	2				0000000001	*|*	0000000000	=	0000000002

999	*|*	909	=	1359				0001101000	*|*	0001020200	=	0001212100

14	*|*	14	=	14				0000000112	*|*	0000000112	=	0000000112

2	*|*	1	=	0				0000000002	*|*	0000000001	=	0000000000

1	*|*	1	=	1				0000000001	*|*	0000000001	=	0000000001

3	*|*	0	=	6				0000000010	*|*	0000000000	=	0000000020

13	*|*	8	=	18				0000000111	*|*	0000000022	=	0000000200

17924	*|*	5	=	9329				0220120212	*|*	0000000012	=	0110210112

16	*|*	0	=	23				0000000121	*|*	0000000000	=	0000000212

19	*|*	1	=	10				0000000201	*|*	0000000001	=	0000000101

1234	*|*	49	=	1780				0001200201	*|*	0000001211	=	0002102221

1	*|*	9	=	20				0000000001	*|*	0000000100	=	0000000202

2	*|*	9	=	19				0000000002	*|*	0000000100	=	0000000201

1982	*|*	2010	=	1960				0002201102	*|*	0002202110	=	0002200121

[araver]

Was in the rush to post it before somebody else does and messed up

1982 *|* 2010 = 1960

Here are all the given clues and the result converted to the base-3 system.

21	*|*	7	=	11				0000000210	*|*	0000000021	=	0000000102

17924	*|*	10751	=	851				0220120212	*|*	0112202012	=	0001011112

1089	*|*	121	=	2069				0001111100	*|*	0000011111	=	0002211122

10	*|*	23	=	6				0000000101	*|*	0000000212	=	0000000020

1	*|*	0	=	2				0000000001	*|*	0000000000	=	0000000002

999	*|*	909	=	1359				0001101000	*|*	0001020200	=	0001212100

14	*|*	14	=	14				0000000112	*|*	0000000112	=	0000000112

2	*|*	1	=	0				0000000002	*|*	0000000001	=	0000000000

1	*|*	1	=	1				0000000001	*|*	0000000001	=	0000000001

3	*|*	0	=	6				0000000010	*|*	0000000000	=	0000000020

13	*|*	8	=	18				0000000111	*|*	0000000022	=	0000000200

17924	*|*	5	=	9329				0220120212	*|*	0000000012	=	0110210112

16	*|*	0	=	23				0000000121	*|*	0000000000	=	0000000212

19	*|*	1	=	10				0000000201	*|*	0000000001	=	0000000101

1234	*|*	49	=	1780				0001200201	*|*	0000001211	=	0002102221

1	*|*	9	=	20				0000000001	*|*	0000000100	=	0000000202

2	*|*	9	=	19				0000000002	*|*	0000000100	=	0000000201

1982	*|*	2010	=	1960				0002201102	*|*	0002202110	=	0002200121

This is correct now.

Congratulations

[araver]

Marking it as solved.

[araver]

Seems I forgot how to mark something as solved

[plainglazed]

nice solve k-man and a frustratingly fun puzzle araver.

was in a nightmare involving a one armed, three thumbed alien with two mouths and no teeth.

EDIT: put in spoiler format for the fun of it

Edited December 3, 2010 by plainglazed

[bushindo]

1982 *|* 2010 = 16

The aliens had the numbering system with the base 3, so they only had digits 0, 1 and 2. Operation *|* is performed on each corresponding digit of a number in the following manner - if the 2 digits are the same then the result is the same (e.g. 0 *|* 0 = 0, 1 *|* 1 = 1, 2 *|* 2 = 2). If the digits are different, the the result is the 3rd remaining digit (e.g. 0 *|* 1 = 2, 1 *|* 2 = 0, 0 *|* 2 = 1). To compute the result for any 2 numbers first convert the numbers to base 3 representation and then apply the operation digit-by-digit. For example,

    012001

*|* 012122

    ------

    012210

Good job, k-man. I'm very impressed that you solved this problem. Would you mind sharing your thought process when approaching this problem? What sort of test did you run on the examples? How did you narrow down the possible solutions, and what was the insight that allowed you to crack the code? Again, great job!

[k-man]

Good job, k-man. I'm very impressed that you solved this problem. Would you mind sharing your thought process when approaching this problem? What sort of test did you run on the examples? How did you narrow down the possible solutions, and what was the insight that allowed you to crack the code? Again, great job!

It was probably more luck than anything else. From several examples I noticed that the operation may create a result that's greater, in between or smaller than the operands. That made me thinking of some sort of binary nature of the operation (similar to binary OR, AND or XOR). So, for a while, I've been using the binary representation of the numbers trying unsuccessfuly to figure out the binary operation that would produce these results. That made me think that some other numerical system may be involved. So, I just decided to try the base 3 system. Once I converted the numbers to base 3 it became quite obvious what the operation does.