Consensus is not a key part of a solution

It does sound counter-intuitive.
However, if you are working in a group, a consensus is not required to solve a problem. It simply is true, not everyone needs to agree on a solution for a problem for it to be solved. In fact, the opposite is true. In coming out with a compromise solution, a solution that everyone can agree on, that solution may not solve the problem in it's entirety. Think of where it came from. A solution that was compromised.
There is this challenge facing teams and groups working to solve a problem every where. The question they wrangle with is: how important is an agreement between all members of the team to solving the problem. The answer will vary from problem to problem. Most groups come to the immediate conclusion that a consensus is very important and often the most important thing. Some groups consider achieving the solution's objectives is more important than a consensus.
But the answer's contribution towards the solution is far less important than most people think. What is more important to a successful solution is ownership of the problem. Owning the problem means taking responsibility to define a problem, lead in the quest for a solution and steer the effort to make the solution a reality. Too many problems get bogged down in the quest to reach a consensus. Time is lost and solutions may not be timely. There can be always a difference of opinion no matter how small. Too much time can be spent on trying to reach a common ground.
What every problem needs is a leader taking charge and solving the problem  There is the key word. Leadership. Even when the problem is faced by a group, a leader must emerge to solve the problem or will emerge by the time the solution is finished. Every group will have people who follow and those who lead or at least want to. A leader here is not one person per se but could also be different people at different stages or according to their capabilities. The leader will be defined not only their ascendancy but also by the followers who choose them. Members of a group must be ready to take on the challenge of leadership and the challenge of being a contributing team member. The scope of how to become that leader is beyond the scope of this post and will be touched on in the future. But it's worth noting that the first step that a leader should take is acknowledge the members of his team and the roles they play.
By refocusing your energy on either taking charge or following and working with the leader, it will ensure the effort to solve the problem keeps moving forward towards the solution.