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i should warn you this is a very evil puzzle. if you solve this you are officially a genius.

11 ? 3 = 2

17 ? 13 = 10

13 ? 17 = 10 <-- yes it's transitive.

23 ? 29 = 29

37 ? 29 = 25

59 ? 47 = 65

I'll post a hint next week if no one gets it.

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I don't want to sound like a troll, and I don't claim to have any copyright or something, but could you not have entitled it differently than Or added a number to it, so that titles don't coincide?

a ? b = b ? a denotes commutativity.

Transitive relations (not operations) are a different thing, see here.

Edited by araver
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Hey!

We had great fun trying to solve this today, but, sadly, nothing came of it, and it looks like we'll need to wait out for the hint!

We have a question though, is the mystery thing literally an operation, such as ">" or "<" or "-" or is it a multitude of operands, such as "*100+10-9"

Thanks, Kris

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okay here's hint #1

it had nothing to do with multiplication, addition, subtraction, or division.

its more like binary xor. except its not binary, nor is it xor.

Edited by phillip1882
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Still nothing, any more hints?

I seem to be lead/drawn towards base 9.

Oh, and all of the numbers you give us before the operation are primes, and all the results are the sum of 2 square numbers.

Hmmm.

Kris

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