Answer:
12 full levels
Step-by-step explanation:
There are multiple ways to do this, what I prefer is recursion
Let's define a equation which helps us determine the number of toothpicks of a pyramid with x levels f(x)
f(1)=3
f(2)=9
f(3)=18
f(4) =30
Etc Etc...
Eventually we can see that for every level x×3 toothpicks are added to f(x-1), so
f(x) = 3*x + f(x-1), so this becomes a geometric sequence 3*(1+2+3...+x)
Now we want to find out how many levels 250 toothpicks can make
250=3*(1+2+3+4..+x)
250/3 = 1+2+3...
I assume you want full levels so I will round down the answer, the closest you can get to 250/3 is (1+2+3...12)
So 12 full levels and a bit of extra toothpicks left
