The relative numbers depend on the setup. For example a pre-gunpowder fortress was usually considered to require an enemy numerical supremacy of 10:1 in men and specific ranged weapons such as crossbows, great crossbows/esprignals/ballistae/oxybeles and stone throwers (trebuchet, giant crossbow, and so on).
The rule of thumb of 3:1 advantage for offensive operations pertained throughout WWI and WWII. But now we have the 21st century, a shift in weapons by increased use of complex programmed devices with sensors and great accuracy. I think this is similar to the shift from expensive heavy gendarmes to reiters that often bested them at a fraction of the cost and maintenance in the 16th century.
The characteristic of modern warfare is that you can kill all you can see within more or less time. If both parties are under observation the shorter OODA loop wins. If one side is able to hide they can use a longer OODA loop without running into danger.
Tanks, the essence of heavy troops have a very short OODA loop of being capable to engage an enemy with their guns. But I think you could replace them with artillery connected to a real time target information stream from an advancing light, but mechanized force with UAV support that is able to deal with infantry, mines and IED while calling in precise artillery strikes the moment they encounter too strong resistance. For such a force, traditionally the use of terrain has been paramount, but modern munitions negate much adavantage from this, so the question is rather how to run the longest range reconnaissance. In my opinion a combination of commandos, artillery, ground attack aircraft and medium infantry will be the economic choice for what previously has been done by heavy forces with armour being increasingly replaced by softkill measures. Medium infantry would be the US Stryker forces for example.