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Go to solution Solved by curr3nt,

## Question

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

## Recommended Posts

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• Solution

Started with prime - 1

83 *&* 13 = 94 --- (83-1) + (13-1) = 94

So went with N - ? for each number

Started filling in the ones with prime numbers

20 *&* 5 = 12 --- (20-12) + (5-1) = 12

8 *&* 31 = 34 --- (8-4) + (31-1) = 34

80 *&* 31 = 62 --- (80-48) + (31-1) = 62

71 *&* 40 = 86 --- (71-1) + (40-24) = 86

50 *&* 11 = 30 --- (50-30) + (11-1) = 30

The ? shares some common denominators

Except 15 *&* 2 = 9 --- (15-7?) + (2-1) = 9

Which I pretended wasn't there...

Figured

22 *&* 12 = 14 --- (22-12) + (12-8) = 14

44 *&* 47 = ? --- (44-?) + (47-1) =

Guessed ? was 24 from 22 *&* 12 = 14

Making

44 *&* 47 = ? --- (44-24) + (47-1) = 66

Basically... not sure how it works. I'm just making things up.

Edited because tabs do not work, neither do spaces...

Edited by curr3nt
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• 0 Is this operation commutative?

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Is this operation commutative?

That is a very quick question Edited by araver
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• 0 I notice that only a few numbers on this chart are not divisible by four, is this... coincidence?

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

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• 0

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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• 0 ##### Share on other sites
• 0 Is the operation singular or multiple operations in a single item?

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• 0

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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• 0 Thanks

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

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• 0

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

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

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

Okay, thanks.

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

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• 0

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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• 0

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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• 0 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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• 0

```
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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