Return to Answer

PHP (60)

Assuming the input is provided in the commandline:

for(;$i<702;)$s.=chr(96.5+sqrt($i+=2));echo$s!=$argv[1]?:42;

Explanation: you can view the string as a triangle structure.

j     i   val
0     0   a
1   1-2   bb
2   3-5   ccc
3   6-9   dddd
4 10-14   eeeee
5 15-20   ffffff
      ...

Line j starts at index i = j*(j+1)/2 (that's the triangular number formula). Solving the quadratic equation results in index i being on line j = int((sqrt(8*i+1)-1)/2) and therefore containing character 97 + int((sqrt(8*i+1)-1)/2). The 0-350 index range allows us to simplify that to 96.5 + sqrt(2*(i+1)), but that no longer holds true for larger values.

Edit: Switched to commandline input as suggested in the comments.
Edit: Uses ternary operator to save a character

PHP (60)

Assuming the input is provided in the commandline:

for(;$i<702;)$s.=chr(96.5+sqrt($i+=2));echo$s!=$argv[1]?:42;

Explanation: you can view the string as a triangle structure.

j     i   val
0     0   a
1   1-2   bb
2   3-5   ccc
3   6-9   dddd
4 10-14   eeeee
5 15-20   ffffff
      ...

Line j starts at index i = j*(j+1)/2 (that's the triangular number formula). Solving the quadratic equation results in index i being on line j = int((sqrt(8*i+1)-1)/2) and therefore containing character 97 + int((sqrt(8*i+1)-1)/2). The 0-350 index range allows us to simplify that to 96.5 + sqrt(2*(i+1)), but that no longer holds true for larger values.

Edit: Switched to commandline input as suggested in the comments.
Edit: Uses conditional operator to save a character

PHP (61)

Assuming the input is provided in the commandline:

for(;$i<702;)$s.=chr(96.5+sqrt($i+=2));echo($s==$argv[1])*42;

Explanation: you can view the string as a triangle structure.

j     i   val
0     0   a
1   1-2   bb
2   3-5   ccc
3   6-9   dddd
4 10-14   eeeee
5 15-20   ffffff
      ...

Line j starts at index i = j*(j+1)/2 (that's the triangular number formula). Solving the quadratic equation results in index i being on line j = int((sqrt(8*i+1)-1)/2) and therefore containing character 97 + int((sqrt(8*i+1)-1)/2). The 0-350 index range allows us to simplify that to 96.5 + sqrt(2*(i+1)), but that no longer holds true for larger values.

Edit: switched to commandline input as suggested in the comments.

PHP (60)

Assuming the input is provided in the commandline:

for(;$i<702;)$s.=chr(96.5+sqrt($i+=2));echo$s!=$argv[1]?:42;

Explanation: you can view the string as a triangle structure.

j     i   val
0     0   a
1   1-2   bb
2   3-5   ccc
3   6-9   dddd
4 10-14   eeeee
5 15-20   ffffff
      ...

Line j starts at index i = j*(j+1)/2 (that's the triangular number formula). Solving the quadratic equation results in index i being on line j = int((sqrt(8*i+1)-1)/2) and therefore containing character 97 + int((sqrt(8*i+1)-1)/2). The 0-350 index range allows us to simplify that to 96.5 + sqrt(2*(i+1)), but that no longer holds true for larger values.

Edit: Switched to commandline input as suggested in the comments.
Edit: Uses ternary operator to save a character

PHP (71)

function _($a){for(;$i<702;)$s.=chr(96.5+sqrt($i+=2));echo($s==$a)*42;}

Explanation: you can view the string as a triangle structure.

j     i   val
0     0   a
1   1-2   bb
2   3-5   ccc
3   6-9   dddd
4 10-14   eeeee
5 15-20   ffffff
      ...

Line j starts at index i = j*(j+1)/2 (that's the triangular number formula). Solving the quadratic equation results in index i being on line j = int((sqrt(8*i+1)-1)/2) and therefore containing character 97 + int((sqrt(8*i+1)-1)/2). The 0-350 index range allows us to simplify that to 96.5 + sqrt(2*(i+1)), but that no longer holds true for larger values.

PHP (61)

Assuming the input is provided in the commandline:

for(;$i<702;)$s.=chr(96.5+sqrt($i+=2));echo($s==$argv[1])*42;

Explanation: you can view the string as a triangle structure.

j     i   val
0     0   a
1   1-2   bb
2   3-5   ccc
3   6-9   dddd
4 10-14   eeeee
5 15-20   ffffff
      ...

Line j starts at index i = j*(j+1)/2 (that's the triangular number formula). Solving the quadratic equation results in index i being on line j = int((sqrt(8*i+1)-1)/2) and therefore containing character 97 + int((sqrt(8*i+1)-1)/2). The 0-350 index range allows us to simplify that to 96.5 + sqrt(2*(i+1)), but that no longer holds true for larger values.

Edit: switched to commandline input as suggested in the comments.