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Mystery Operation III

We've barely started exploring our solar system when a message is received from outer space.

It looks like an encoded operation is embedded in the message. And it also looks as it is a test of some sort.

```
4 *&* 8 = 6

20 *&* 5 = 12

8 *&* 31 = 34

-------------

44 *&* 47 = ?

```

Maybe we ought to respond to it?

What do you think?

P.S. General rules are the same as in and

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Posted · Report post

Is this operation commutative?

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Posted (edited) · Report post

Is this operation commutative?

That is a very quick question

Edited by araver
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I notice that only a few numbers on this chart are not divisible by four, is this... coincidence?

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I notice that only a few numbers on this chart are not divisible by four, is this... coincidence?

Coincidence. Noted and I will add another example shortly...

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```
4 *&* 8 = 6

20 *&* 5 = 12

8 *&* 31 = 34

15 *&* 2 = 9

-------------

44 *&* 47 = ?

```

It is commutative.

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Posted · Report post

If eight were the second number in any other group would the group end up with a result around six?

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If eight were the second number in any other group would the group end up with a result around six?

Sorry, I can't really answer that as it looks like a shot in the dark. And please use spoilers.

Adding another example to the challenge:

```
4 *&* 8 = 6

20 *&* 5 = 12

8 *&* 31 = 34

15 *&* 2 = 9

80 *&* 31 = 62

-------------

44 *&* 47 = ?

```

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Is the operation singular or multiple operations in a single item?

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Posted (edited) · Report post

Is the operation singular or multiple operations in a single item?

I'm not sure I understand the question right as there is no example of "singular operation on a single item" for a binary operation I know of:

- multiplication is basically one operand added multiple times (times the other operand)

- exponentiation is basically one operand multiplied with itself multiple times (times the other operand)

- addition is basically one operand increased by 1 (times the other operand)

So, the mystery operation is a binary operation i.e. a function that takes two numbers and returns another number.

Edited by araver
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Thanks

To clarify, I was asking if it performed several operations at once.

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Adding another example to the challenge:

```
4 *&* 8 = 6

20 *&* 5 = 12

8 *&* 31 = 34

15 *&* 2 = 9

80 *&* 31 = 62

71 *&* 40 = 86

-------------

44 *&* 47 = ?

```

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I'm still completely losing the solution of this puzzle.

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```
4 *&* 8 = 6

20 *&* 5 = 12

8 *&* 31 = 34

15 *&* 2 = 9

80 *&* 31 = 62

71 *&* 40 = 86

83 *&* 13 = 94

-------------

44 *&* 47 = ?

```

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Posted · Report post

Any particular reason that none of the numbers involved are negative?

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Any particular reason that none of the numbers involved are negative?

Maybe. But I usually use non-negative integers in my Mystery Ops so far.

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Maybe. But I usually use non-negative integers in my Mystery Ops so far.

Okay, thanks.

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Okay, thanks.

If you were asking if the operation can be applied on negative numbers as well, then ... it could.

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This is an excellent puzzle araver, I usually pick patterns up quickly. I still can't find this one.

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Adding another example to the challenge:

```
4 *&* 8 = 6

20 *&* 5 = 12

8 *&* 31 = 34

15 *&* 2 = 9

80 *&* 31 = 62

71 *&* 40 = 86

83 *&* 13 = 94

50 *&* 11 = 30

-------------

44 *&* 47 = ?

```

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Okay - maybe time for some group think. some thoughts in the following spoiler so if you dont care to see. strictly fwiw...

every case except the first and including the case to solve contains a prime number. seems too much of a coincidence not to be relevant unless it's just meant to distract. have been playing with factors and combinations with no luck so far.

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I've been playing with this one as well, but I don't have a strong math background so most of the puzzles in this section elude me.

I first tried experimenting with bases, but since the last puzzles were based related, I thought this would be different. I also noticed the primes and my "gut" feeling is that the solution is related to factoring. I factored all the problems and noticed a few patterns but nothing concrete. I think I just have not gone far enough with the math.

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Posted (edited) · Report post

```
4 *&* 8 = 6

20 *&* 5 = 12

8 *&* 31 = 34

15 *&* 2 = 9

80 *&* 31 = 62

71 *&* 40 = 86

83 *&* 13 = 94

50 *&* 11 = 30

40 *&* 42 = 28

-------------

44 *&* 47 = ?

```

And secretly

enjoying that there there are at least three people thinking on this.

But that's not a secret anymore since you opened the spoiler

EDIT: Spelling

Edited by araver
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54?

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