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I once saw a science program with the danish astrophycisist Jens Martin Knudsen, who said that there exists seven absolutely fundamental constants of nature, and if one of these were changed ever so slightly, it would lead to drastic changes in the whole universe. So my question is: what is the smallest set of physical constants, by which all other contants of nature, in principle, can be derived? How many are needed? I know the set is probably not unique, but a sensible set then. I guess three of them would be the speed of light in vacuum, Plancks constant and Newtons gravitational constant.

Thanks in advance!