 This is the puzzle we are going to solve.
If this is your first time solving this type of puzzle, it is recommended that you learn how to solve a Griddler before trying a Triddler. 
 We will start with the clues 4 and 7 (circled in red).
The black triangles are placed using overlapping counting. For a detailed explanation of this method, see the Griddlers Tutorial.
The green arrow marks the direction of the clues as well as the direction of the colored triangle chains. 
 We are now going to look at the entire top line, from left to right:  2   We leave one triangle empty above and below the black triangle and color the rest of the line white (the background color).  2   We already have 2 black triangles as required so we can color the rest of the line white.  2   Is still empty.  7   We can add 3 black triangles below the 2 that are already in the grid, leave 2 empty and color the rest white.  2   The first and second clues are 2. Since we have 2 black triangles, we can fill one triangle above and below the doubleblack in white . It leaves us one triangle above the white (it is marked with a red dot). We can color this white since it is only 1 triangle and the clue calls for 2.  2   The first clue is 2. Since we already have 2 triangles in the grid, we can fill one triangle above and below the doubleblack with white.  
 Again, let's look at the whole line, from top to bottom:  7   We can mark 6 black triangles in addition to the one we have and complete the line with white background color since we have a total of 7.  2   Below the 2 black triangles we can color one triangle white. Since this must be our first chain of two, we can color the very first triangle white.  2   Same as above.  2   Same as above.  5   We can complete the "chain" of 5 as required and mark, in white, one triangle below the 5 blacks.  
 Now we can solve the left side, from top to bottom:  1   We will color the one empty triangle black.  4 , 7   This line contains all the necessary triangles so we can color the one remaining empty triangle white.  3 , 1 , 2   The first 3 and the last 2 black triangles are already in the grid so we can mark off their boundaries with white. That leaves only one empty triangle for the middle clue of this line. We color it black.  2 , 1 , 2   We color the triangle to the left of the 2 blacks with white.  2 , 2 , 2   The clue requires 2. We can add first one black triangle and then one white triangle to the left of the what is now 2 blacks.  
 From left to right:  2   The required 2 is already in the grid so we can color the rest of the line white.  7   We can add 2 black triangles to the 5 that are already in the grid and color the rest of the line white.  2 , 2 ...   The first "chain" of 2 is in the grid. The triangle with the red dot was empty but, since the next clue is 2, we can now color it white.  2 , 1 ...   We add one white triangle below the 1 black square.  
 7   We add 4 black triangles to the three we already have and color the rest of the line white.
The line that is marked with a green arrow is empty so we can color all the triangles white. 

 From top right to left bottom:  2 , 1 , 2   There is only one triangle left. From the middle clue we have to color it black.  2 , 1 , 2   All the clues are in the grid so we can color in the rest of the line white.  2 , 2 , 2   We color the triangle above the two blacks with white.  3 , 7 , 1   We can now complete the 7 required blacks and end the chain with a white triangle.  
 From top to bottom:  2 , 1 , 2   All the clues are in the grid so we can color the rest of the line white.  2 , 2 , 2   We color the triangle to the right of the first 2 blacks with white. That leaves us with three empty triangles. We can mark the triangle in the middle with black.  2 , 2   All the clues are in the grid so we can color all the empty triangles white.  1 , 7   We can complete the 7 required blacks and end the chain with a white triangle.  
 2 , 2 , 2   There is only one empty triangle left in the grid. Since the clue is 2, we color it black.
 5 , 2   All the clues are in the grid so we can color the rest of the line white.  
 2 , 1 , 1 , 2 , 1 , 1 , 1  Fill in the remaining clues and background triangles. 

 From top to bottom:
 1 , 2   We color the rightmost empty triangle white because the first right clue is 2. We can therefore also add one black triangle to the one that is already in the grid, and one white to its left.
 1 , 2 , 1   We can't know where to put the rightmost 1 clue, but we sure know that the black triangle in the middle is the one for the second clue (2). We can therefore add one black triangle to its left and end the chain with white.  
 3 , 7 ,1   We can color the one empty triangle in black as required.
 1 , 2 , 1   The first right clue is one (the 1 we've just added) so we can color, with white, the triangle to its left (marked with a red dot).  
 2 , 1   We color the one triangle at the bottom in black and complete the line with white.


 2 , 1   Since we have one triangle at the right, we can color the triangle to its left white. We can add one black triangle to the one in the middle to create the "chain" of 2 required, and complete the line with white.  
 2 , 2 , 1 , 1 , 1   The first two clues are already in the grid. The only way to put in the triple "1" is as marked in red on the picture. That completes the puzzle. 

 This is the solution of the KITE puzzle. 
