What is the least number of colors you need to correctly color in the sections of the pictures so that no two touching sections are the same color?

8 colors

Step-by-step explanation:

There should be at least 8 different colors available for coloring the sections. The one color is used to color all the small triangles on the upper most and lower most lines, then there will be required another color so that the edges does not matches with the previous color. For the bigger hexagon shapes in the center we will require different colors for all of them because all of the hexagon shapes touches a line and an edge with each other.

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )