Is this a Cayley type table ?

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Hypatia001

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Hello all.... once again i need help understanding this question. I have a table which i think is a cayley type but i do not know how they work or the rules around them. Can anyone help ?
 
Hypatia001 said:
Thanks.... but what does that even mean ? Please treat me as a maths dummy (which i am)... i obviously get the 7*5 part... but how does the modulo mean ?
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The modulo produces the remainder of an integer division. 35 divided by 12 give you a remainder of 11, so 35 mod 12 = 11.
Another example, 8 divided by 12 gives you the remainder of 8, thus 8 mod 12 = 8. In simple terms, 35 mod 12, ask yourself what is the remainder when I take 35 divides by 12?
You can learn more about it here: https://brilliant.org/wiki/modular-arithmetic/
 
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Hypatia001 said:
Thanks.... but what does that even mean ? Please treat me as a maths dummy (which i am)... i obviously get the 7*5 part... but how does the modulo mean ?
BigBeachBanana said:
Multiply then modulo 12. For example, 7*5=35 and 35 mod 12 = 11.
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I do not want the answer but to understand how to solve this type of question... i know i am looking for a pattern .. and am trying to see what the 0 and 1 lines should be too.
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i see.... its about patterns !!! Looking for the common way to get the answers in the boxes
 
Hypatia001 said:
i see.... its about patterns !!! Looking for the common way to get the answers in the boxes
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What you haven't told us is the context of the problem. That can make a huge difference in the kind of answers you get.

Since you mentioned Cayley tables, one would guess that this came from a class that might also have taught about modular arithmetic. But it appears that it was just a puzzle with no such context.

And in that case, there is no method; what to try depends on what ideas you happen to have. In fact, if you were just given the table and expected to guess what it means, there is really no one correct answer (though the answer you were given seems certainly what they had in mind).
 
Dr.Peterson said:
What you haven't told us is the context of the problem. That can make a huge difference in the kind of answers you get.

Since you mentioned Cayley tables, one would guess that this came from a class that might also have taught about modular arithmetic. But it appears that it was just a puzzle with no such context.

And in that case, there is no method; what to try depends on what ideas you happen to have. In fact, if you were just given the table and expected to guess what it means, there is really no one correct answer (though the answer you were given seems certainly what they had in mind).
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There was no other infor.ation. i have seen such tables before but never u derstood or researched them. Clearly its a pattern of some sort but intil someone shines a light on it i am pretty much in the dark. Now i understand the mechanism.
 
6*7 = (2*3)*7 = 2*(3*7). Now use the table to to do this multiplication.
6*7 = (3*2)*7 = 3*(2*7). Now use the table to to do this multiplication.
You do not even have to know that the multiplication is being done in mod 12. You just have to know how to use the associative law!

Although you should know that the multiplication is being done mod 12, you should still compute 6*7 using the table and only the table. I could be wrong, but I think that the author of this problem wants you to use just the table.

What answer do you get along with your work from using the table.

EDIT: Ouch, the table does not give the information to compute 6*7 like I described.
If it did, this is how it could be done.
6*7 = (2*3)*7 = 2*(3*7). From the table, 3*7=9. Now using the table, compute 2*9 which is NOT on the table.
 
Hypatia001 said:
There was no other infor.ation. i have seen such tables before but never u derstood or researched them. Clearly its a pattern of some sort but intil someone shines a light on it i am pretty much in the dark. Now i understand the mechanism.
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I have to ask again, what is the context of the question? That is, where did it come from?

Did you just find a piece of paper lying on the ground that said this, or is it associated with a class you are taking, or a puzzle from your child's class, or what? Do you know anything about finite groups or such? Any information like that can give us some sense of what is expected, so we aren't left to guess blindly.

Technically, it isn't a Cayley table, which has to be complete. It is just a partial multiplication table. And given that you know nothing about modular arithmetic, if nothing was stated about what "multiplication" means here, we really don't even know that this multiplication is associative or commutative as Steven G is assuming! (I think he has a good idea, but he's still guessing about the intent of the problem.)
 
Yes, I assumed that the table was associative and commutative. I know that I had no right to make such an assumption but with what was given what else could I do? This is why we ask for and need the complete problem and where it came from.
 
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