Algorithm to define min-Max ranges with some defined bound Having to populate the following table of MIN-MAX cells, starting with only the knowledge of the IC value

I was thinking about a formula to get the values of A, B, C, D, E, F, G
which works also for the values of IC and 2xIC
I'm able to get the values from 0 to IC using the following formula:
$$K = 3$$
$$LEVEL.MIN = \frac{IC}{K} \times (LEVEL-1)$$
$$LEVEL.MAX = \frac{IC}{K} \times (LEVEL)$$
I need another similar formula for the values of E, F, G, 2xIC.
Maybe, since $E=IC$, the formula should have $+IC$ as a fxed part.

Let's look at the conditions that you gave. You say that the MIN of level $n$ should be equal to the MAX of level $n-1$. Using this condition, we should rename the variables like so:


*

*Level 1: MIN = 0, MAX = A

*Level 2: MIN = A, MAX = D

*Level 3: MIN = D, MAX = E= IC

*Level 4: MIN = E, MAX = G

*Level 5: MIN = G, MAX = 2IC = 2E


The next condition is that each level from 1 to 3 needs to have the same difference between MAX and MIN. In other words,
$$
A = D-A = IC-D
$$
From this condition we see that $D = 2A$ and of course $$A=IC-D \qquad \Rightarrow \qquad D = 2IC - 2D \qquad \Rightarrow \qquad 3D=2IC$$
The next condition is that levels 4 and 5 need to have the same difference between MAX and MIN. In other words,
$$
G-E = 2E - G
$$
Adding $E+G$ to boths sides, this is the same as $2G = 3E$. Now we can plug in these results to get the new level hierarchy: 


*

*Level 1: MIN = $0$, MAX = $A$

*Level 2: MIN = $A$, MAX = $2A$

*Level 3: MIN = $2A$, MAX = $IC$

*Level 4: MIN = $IC$, MAX = $\frac{3}{2} IC$

*Level 5: MIN = $\frac{3}{2} IC$, MAX = $2IC$
With these conditions, the hierarchy is left with two free variables, IC and A. But otherwise, the hierarchy now follows the conditions that you gave.
