This map is very similar to map 37, however there is no shaman on this map.
With the cheese barely out of reach, unlike map 35, the platform needs to be unbalanced a little bit so that one side will be raised and the cheese can be obtained. The side with the least mice will naturally be closer to the cheese, so stick with that. Try not to tilt the plank too much or else mice will go flying off and the plank may fall off the screen, causing many deaths of mice.
The two sides will need to be imbalanced. The side with the most mice will be closer to the cheese and get it first. The other side will be lower and the platform will probably fall before they have the chance to get the cheese again.
There is no shaman on this map.