## Trigons

 ``` .--A--.--B--. / \ / \ / \ C D E F G H .--I--.--J--.--K--. / \ / \ / \ / \ L M N O P Q R S .--S--.--T--.--U--.--V--. W X Y Z a b c d \ / \ / \ / \ / .--e--.--f--.--g--. h i j k l m \ / \ / \ / .--n--.--o--. ``` Trigons are similar to Triominos, except instead of having numbers at each corner, the numbers are on the sides of each triangular piece. Can you take a set of 24 trigons, consisting of all possible configurations of the values 0, 1, 2, and 3, and place them into a hexagon, two units on a side, such that each adjacent side matches correctly? Or, show why it can't be done. (Note that 1-2-3 is a different trigon than 1-3-2, since neither can be rotated to create the other; while 1-1-2 would be the same as 1-2-1, since the latter can be rotated to obtain the former.)
Since I think the above problem may be easily solved, consider the following extension puzzles:
• Try to solve the puzzle, making the sum at the 7 internal points the same (the sum of the six numbers surrounding the 7 internal points).
• Try to solve the puzzle, making the six internal trigons have different sums. (The sum of the three numbers on each trigon.)

Source: Original, based on a puzzle in Dell's Math Puzzles and Logic Problems magazine.

Solution
Mail to Ken