The White triangle is similar to the Red triangle
As ratio of areas = ratio of bases when height is same,
Ratio of sides is 2:3
White triangle = 9/4 * Red triangle = 9/2

Thus the Green Region = 5.5 units.

Route66

30(sum of corner of triangle)

For a change

34

6

5*6+2=31,7*6+2=44

13

First the logicians will have to take a leap of logic. The master has told them that it won’t be impossible for any logician to solve the puzzle. Thus it is assure that any of the color can’t exist only once. If it did, the one wearing it will have no clue about that color which would be unfair for him.

Now every logician will look around in the circle and count the number of times they see a particular color. If a color is seen only once, then the logician will know that the color on his band must be of the same color (as per the leap of logic). And then the logician will leave on the first bell.

In the similar fashion, any logician who see any color just once will be able to identify his own color and they will leave when the bell rings or they will be disqualified and asked to leave. Equivalently, any color for which there are two bands, will be eliminated after the first bell has rung. Thus there must be three bands of any remaining color at least.

Assume that a logician don’t see any color once, but sees a color twice. If they were the only bands of this color then the two logicians must have left at the first bell. But they did not. Thus it means that his band color is the same and he will leave on the second bell.”

210+6

The second digit in each set is 6.
If you add the numbers, you will find that they add up to be the cube of 2, 3, 4 and 5.

The next number is 6 and the cube of 6 is 216.

Thus, the last set will be (210 + 6).

The code can be decrypted to sound as “U four seven two B M T”.
The code is U472BMT.