This is from an old math olympiad question
You have the following relationships:
2T4 = 3
T7 = 5
T4 = 4.5
T6 = 3
What is the value of 6T10?
A. 16
B. 3
C. 5
D. 8
E 10.5
I know which of the above choices is the answer, but I can’t figure out why.
I’m not sure I understand… Is T meant to be some unspecified operator? If so, is it a unary or binary operator? There’s apparently some meaning both to 2T4 (a binary usage) and to T7 (a unary usage), which would mean the operator must have two different (though probably related) meanings in different contexts. Unfortunately, we only have one example of the binary context, which isn’t nearly enough information to determine its meaning in that context, which is what we need for the answer.
Well, I had thought that perhaps you were to use the previous answer in the next one. My reasoning was that 2T4=3 meant that T was some sort of an averaging function. If you put 3 in the next one, you get 3T7=5, which fits the pattern. 5T4=4.5 works likewise, except the bigger number is first, a difference. 4.5T6=3 does not work with this pattern, unfortunately.
6T10 would fit with the answer D. 8, but as the last clue doesn’t work with the pattern, I doubt that’s it.
Polerius
Well, before this thread “dies”, what do you think the answer is and are you sure you didn’t make a typo somewhere?
Well 4.5 IS the average of 6 and 3, which makes wolf_meister’s question important.
I tried finding the answer by Google. No success.
Well
2T4=T6
So I am guessing if you have xTy that equals T(x+y). So 6T10=T16. Now all I gotta figure out is what T does.
It’s tantalizingly close to being a count of letters in the words for the numbers (binary examples notwithstanding).
2T4 = 3 Hmmm, this one doen’t fit.
T7 = 5 “seven” has 5 letters
T4 = 4.5 “four” has 4 letters
T6 = 3 “six” has three letters
I have exactly the same thoughts.
I have not more information than what I wrote in the OP, except for which is the answer.
I’ll go ahead and state that it is D, i.e. 8, since knowing that may help us get closer to solving this. (It hasn’t helped me though 
)
Remarkably close.
The answer is in fact D. 8, but the reasoning has to be something else.
Good question.
I haven’t made a typo, but I’m not sure if there wasn’t a typo in the book where I read this from.
I’m trying to contact someone who might know what the original formulation was.
I’ll keep you posted.
Man this problem is really bugging me. I get the feeling that the answer is going to be something stupid.
Reading this thread, it seems like the question is solved. You deduced two rules:
(1) xTy = average of x and y = (x+y) / 2
and that
(2) Ty means the average of y and the answer from the previous row.
Given that,
6T10 means the average of 6 and 10, or 8. The answers from previous rows don’t apply, because 6T10 is of form(1).
Dang, didn’t see the T6=3. Curses, that is weird.
OK, I’ve gotten the original formulation of the proble, and it indeed is slightly different from the one in the OP.
The original problem is:
"You have the following relationships:
2T4 = 3
T7 = 5
T4 = 4.5
0T6 = 3
What is the value of 6T10?"
So, muttrox’s rules (1) and (2) hold for all given pairs, and they give us the final answer to 6T10 as 8.
This turned out to be much simpler than I thought. If I had known the original formulation I wouldn’t have posted it here. Sorry for any unnecessary frustration
Congratulations to Garfield226 !!!