A piece is missing!
What should it be?
- 5 is diagonal to G, where G is the next letter of F(the first Letter of 5);
- 3 is diagonal to U, where U is the next letter of T(the first Letter of 3);
- 1 is diagonal to P, where P is the next letter of O(the first Letter of 1);
- Therefore answer is T because it is the next letter of S(the first Letter of 7);
I've exhausted my mental state on this one today; my only plausible guess is:
If you convert the letters to their respective numerical placements in the alphabet:
$G = 7$
$P = 16$
$U = 21$
You can use the digits we have $[1, 1, 1, 2, 3, 4, 5, 6, 7, 7]$ to create $\pi$ with some math:
$31415$ is the most obvious. But let's keep going:
$7 + 2 = 9$ so we now have $314159$ which leaves $[1, 6, 7]$.
Knowing the next digit is $2$, we can use our remaining digits to get there: $7 - 6 + 1 = 2$ so we get $3141592$ which is $\pi$ accurate to $6$ decimal places without the decimal point.
Half serious answer:
In LeetSpeek (13375P33K):
G17 == GIT == GET
5UM == SUM == SOME
P13 == PIE
The only thing missing is the letter "M" which AFAIK doesn't have a numerical analogue. (Although this explanation is suspicious because "G" then should have been either "6" or "9", rather than the letter)
Like @Lonewolf 's answer, take the opposite piece's number's first letter ("S"even), then take the next letter alphabetically. I believe he incorrectly took the previous letter of R
EDIT: @Lonewolf corrected his at the same time I posted this!
I believe it's the letter "R"
Kind of like what @lonewolf said but it's the letter before the one that is diagonal. Where "R" is one letter before "S" which the word "Seven" begins with and "P" is across from "1" which is one letter after "O" which the word "One begins with and so on.
1 - 3 : Difference 2
5 - 7 : Difference 2
U - P : Difference 5
G - B : Difference 5
...if that makes any since!
Same reason as @Lonewolf
P comes after O in One, all of the letters are the letter after the first letter of the number
Edit: @kugo2006 posted his answer at the same time I was typing and I didn't notice 'til now that Lonewolf also corrected his