I wrote a post about Monster Levels recently but did not mention the Monster Contest that occurs on 25 Autumn. In this Contest, your most powerful Tame Monster competes against those belong to other unspecified villagers. There is no physical combat or trial of strength. It is simply a matter of 'registering' the strength level of the monster you have chosen to enter. The prize is a 'Health It'.
Herman's instructions for the Contst are a little confusing. He will tell you to:'Please send at least one of your monsters back to the Forest.' At first I thought it would be like the 'Monster Taming Contest' which required a free space in your Monster Barn for the Monster that you tamed in the course of the competition. (I had to free a Monster in order to be able to compete in THAT one, because my Barn had its full quota at the time.)
In fact, I think that Herman's instructions in this first sentence of his probably were supposed to go with the other Contest. In the 'Monster Contest' in Autumn, your entry will be one of your existing Tame Monsters rather than a new one. In fact, as the 'strength' of your Monsters will improve with time and use, it is best to use a Monster who has been tamed for a long time.
You need to ask your Monster first to accompany you. When he/she is outside the Monster Barn, you then need to speak to Monster to discover total Strength. Yu have the option to choose NOT to enter the Monster in the Contest if you wish to see the totals of all your Monsters before you make a final decision. 15 out of 16 of my Monsters were at 46. The Silver Wolf I use in combat always was at 50. As the other monsters never fought with me but only work on the farm and provide Ranch Products, 'Strength' is not earned by combat exclusively but by 'use' of the Monster and Heart Level combined somehow. The other 15 monters ALL had 46 Strength, even though two had been tamed fairly recently, and were of many different varieties... but all were at 10 Hearts.
The prize for winning the Monster Contest is a HEALTH IT. More important a reward for me was the fact that this Festival brought the remaining girls to maximum heart level at 10 Hearts.