# Mystery operation

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

10 *|* 23 = 6

1 *|* 0 = 2


and

17924 *|* 10751 = 851


then how much is:

1982 *|* 2010 = ?


Hint:

The result converted to the base-3 system.

Hint2:

a *|* b = b *|* a

and

a *|* a = a

• Are the numbers same as ours or different i.e our 1 is same as theirs? Commented Aug 22, 2016 at 10:41
• @JasonC just because a puzzle was posted here doesn't mean it a) works or b) is a valid puzzle Commented Aug 22, 2016 at 10:58
• @AmruthA its base 10 converted to base 3, so 851 is 1'011'112 Commented Aug 22, 2016 at 11:09
• Amruth going right direction Commented Aug 22, 2016 at 11:10
• Argh, I really want to give up, but I've dug myself in a hole with all my comments and I have no choice now. :'( Commented Aug 22, 2016 at 11:12

Ok, I think I got something. The answer should be :

1960.

The ancient civilization

had a numbering system based on the base 3, as it has been mentioned in the comments and in the hint. Thus, they only had digits 0, 1 and 2.

The operation *|* is performed :

on each digit of a number like this:
> If the 2 digits are the same, then the result is the same.
That gives us :
0 *|* 0 = 0
1 *|* 1 = 1
2 *|* 2 = 2
> If the digits are different, then the result is the last remaining digit That gives us :
0 *|* 1 = 2
1 *|* 2 = 0
2 *|* 0 = 1

Now, the real problem. In order to obtain the result for 2 numbers, we have to

convert the numbers to their representation in base-3. Then, we apply the operation digit by digit.
For example, 421 *|* 379 gives 120121 *|* 112001 which gives 101211, and converted back to decimal : 292.

And now, all the values in the question :

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

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

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

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

With, of course, the final answer :

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

• Correct answer!!! Commented Aug 22, 2016 at 11:56
• Oh wow... As soon as I saw your answer I immediately understood the pattern... That's frustrating :P
– user14478
Commented Aug 22, 2016 at 11:57
• Good job sir.... I'm very impressed that you solved this problem. but How? Commented Aug 22, 2016 at 11:59
• @Smart I'm not sure if you asked me, but in case you did (to prove I didn't lie in my comment :P): ROT13 Pbaireg rnpu cneg gb onfr guerr gura pbzcner gur gjb cnegf (yrnqvat mrebf) pbyhza-jvfr. Vs gurl ner gjb qvssrerag inyhrf, pubbfr gur erznvavat bar. Vs gurer ner gur fnzr ahzoref, pubbfr gung ahzore.
– user14478
Commented Aug 22, 2016 at 12:03
• @LukasRotter Exaclty! Good job to you :) Commented Aug 22, 2016 at 12:24