Random Puzzles 

Workings

Hint
Convert the letters to positions in the alphabet.

Answer
M.

Reasoning
These are letters that occupy prime number positions in the alphabet:
B =  2
C =  3
E =  5
G =  7
K = 11
M = 13 *
Q = 17
S = 19
W = 23

Workings

Hint
Remember that you can't have three White or Blue squares together in a row or column.

Answer
 

Workings

Hint
Where did Max finish?

Answer
   #1 Logan Green  18
   #2 Kelly Red    24
   #3 Max   Blue   28
   #4 Jesse Yellow 21

Reasoning
By (1), the 18-year-old won the championship.
By (3), Kelly finished second.
By (6), the person who came last was 21.
   #1              18
   #2 Kelly
   #3
   #4              21

By (4), Max was the oldest competitor at 28, and can only have finished third. Which means that Kelly must have been 24.
   #1              18
   #2 Kelly        24
   #3 Max          28
   #4              21

By (2), the person who wore Red can only be 21 or 24, so Max can't have worn Red. Max didn't wear Green (4), and didn't wear Yellow (5), so Max must have worn Blue.
   #1              18
   #2 Kelly        24
   #3 Max   Blue   28
   #4              21

By (5), Kelly didn't wear Yellow, and by (4) didn't wear Green, so must have worn Red.
   #1              18
   #2 Kelly Red    24
   #3 Max   Blue   28
   #4              21

By (2), Jesse was 21. Which means that Logan was 18.
   #1 Logan        18
   #2 Kelly Red    24
   #3 Max   Blue   28
   #4 Jesse        21

By (4), Logan wore Green. Which means that Jesse wore Yellow.
   #1 Logan Green  18
   #2 Kelly Red    24
   #3 Max   Blue   28
   #4 Jesse Yellow 21

Workings

Hint
The answer involves a square root.

Answer
4.

The middle of each triangle contains the square root of the sum of the three surrounding numbers.