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araver

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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 = ?

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araver Veteran

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Posted (edited)

Declaring open-season on questions again :D

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

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 by araver
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araver Veteran

araver

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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

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araver Veteran

araver

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  On 11/29/2010 at 4:45 PM, rajat_magic said:

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

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araver Veteran

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  On 11/29/2010 at 10:17 PM, :-) said:

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

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araver Veteran

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  On 12/1/2010 at 3:12 PM, Molly Mae said:

  Reveal hidden contents

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?

  Reveal hidden contents

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? :D

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

  Reveal hidden contents

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

Also, what are:

1 *|* 9

2 *|* 9

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araver Veteran

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  On 12/1/2010 at 10:58 PM, dawh said:

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

  Reveal hidden contents

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

Also, what are:

1 *|* 9

2 *|* 9

  Reveal hidden contents

Basically yes!

:thumbsup:

The rest:

1 *|* 9 = 20

2 *|* 9 = 19

  On 12/1/2010 at 11:05 PM, k-man said:

  Reveal hidden contents

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?

  Reveal hidden contents

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.

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k-man Proficient

k-man

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  Reveal hidden contents

1982 *|* 2010 = 16

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araver Veteran

araver

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  On 12/2/2010 at 4:08 PM, k-man said:

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1982 *|* 2010 = 16

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

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

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

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1960

I think I got that right... :unsure:

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k-man Proficient

k-man

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

  Reveal hidden contents

1982 *|* 2010 = 1960

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

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araver Veteran

araver

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  On 12/2/2010 at 5:13 PM, k-man said:

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

  Reveal hidden contents

1982 *|* 2010 = 1960

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

This is correct now.

Congratulations :thumbsup:

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bushindo Experienced

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  On 12/2/2010 at 4:08 PM, k-man said:

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1982 *|* 2010 = 16

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!

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k-man Proficient

k-man

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  On 12/6/2010 at 4:36 AM, bushindo said:

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.

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