The second value evaluated within the context of the above formula will provide the required interest rate.

The above formula then is only an approximation, as the calculations become more involved.

The above formula works for any date in the 21st century.

The above formula only detects changes in the positive direction.

Another common mistake is to forget the last in the above formulas.

Results computed using the above formula have appeared in the literature.

We can then take and implement the above formula as follows.

All the above formulae are valid for pure states only.

From the above formula, this only tells us that .

If the first ball was red then the above formula is used with reduced by one.