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Here is the puzzle that has been torturing me for past few hours... I still have not come up with logical solution. here

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The answer is

82617

The first thing you need to realize is that the numbers on the right are not lined up with the items on the left. So MERT does not equal 3174. However, if you look closely at the words, you can see a couple of patterns...

The 2nd letter is limited to E and A, and the 3rd letter is limited to R and S.

By looking at the characters and numbers in those positions, you can see...

That there are 2 A's and 3 E's in the second position of the text, and 2 1's and 3 2's I the second position of the numbers, so there appears to be a direct correlation. 1 = A, 2 = E, and doing the same for the 3rd position, we get 6 = R and 7 = S.

At this point, you don't even need to continue to find the letters, because there is only one of the multiple choice items that fits the pattern once you convert TERAS to the number scheme.

?2617, which is B.

However, if you do continue to expand out, you will finally find that

5 = M, 3 = F, 4 = K, and 8 = T, just by process of elimination. 9 has no corollary in this puzzle.

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    $\begingroup$ It goes even faster if you look at the last numbers (3 T's), which reduces the potential answers to two choices; then look at the first numbers (2 M's), which eliminates one of the two. $\endgroup$ – Hellion Mar 4 '16 at 18:33

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