Question

An odd number of people - each pulling with the same strength - participate in a tug of war game, yet no team wins. How is this possible?

Answer 1

Odd no. of people are pulling with same strength.
Since, there are odd no. of people, if we divide into two groups, the force exerted by one team must be greater than the other team. This implies that the equilibrium of forces is disrupted. So, the team that has more numbers must be able to win.
Yet, no one wins. This can be accounted to the presence of external forces like friction or reaction force from the ground.
The team with lower numbers must have a higher coefficient of static friction which increases the opposition to their motion. Hence, a new equilibrium is established with friction's involvement.
Also, the players exert a force on the ground when they push their legs on it. The ground, according to Newton's third law exerts an equal and opposite reaction force. If the players of the team with lesser numbers push the ground hard enough, they can get the help of ground's reaction force to oppose other team's endeavor.