Is this usage of "reign" correct?

Solution 1:

The NOAD reports the following note, in the definition of reign:

The correct idiomatic phrase is free rein, not free reign.

In the definition of rein, the dictionary adds the following notes:

The idiomatic phrase a free rein, which derives from the literal meaning of using reins to control a horse, is sometimes misinterpreted and written as a free reign. More than a third of the citations for the phrase in the Oxford English Corpus use reign instead of rein.

Grammatically speaking, both the phrases would be correct, but the idiomatic phrase should be free rein.