The Unsolvable Problem

Mental Flexibility in Grappling

This is a key lesson to learn in battle of any kind and is particularly appropriate to the way I approach application of Brazilian Jiu-Jitsu technique to a fight or sparring match.

To achieve success in battle, you must present a dazzling flexibility to both respond to attack and counterattack with a level of speed and complexity that off-balance your opponent in a way that prevents them from ever gaining stable ground to continue the fight. A good example of this is the concept of “overwhelming display of force” that Special Forces military units specialize in. They create a problem that off-balances the enemy to such a degree that they are too busy running for cover to ever successfully form an offensive. Another example of this is a skilled debater who subtly changes their verbal attacks faster than their opponent can respond to the logical twists of reason that they are presented with. In both cases, the victorious has presented an unsolvable problem for their opponent.

The details of this concept of an unsolvable problem need to be considered in terms of the parameters present, which includes the timeframe and other “characteristics of the battlefield problem.”


Your opponent represents the enemy if you extend the concept of martial arts sparring to real battle. Each position your opponent presents and each attack they launch poses a specific problem for you that is framed in time. This timeframe can be split into a series of discrete moments:

  1. When the attack is launched or position is established. This is a moment of transition which can either be in the form of an initial attack or a new position in a series of maneuvers.
  1. When you detect the attack or position.
  2. Mental reflex: How your detection of this affects your mental state.
  3. Physical reflex: What your physical reaction is to this attack before it impacts you.
Continuation or termination
  • Impact of damage on you if the attack succeeds, or impact on your opponent if your response (evasion or counterattack) succeeds.
  • And so on… Unless your response terminates the attack, your response will create a problem for your opponent to solve (a counterattack or new position).

Parameters: Characteristics of the Problem

Each problem has a number of parameters, or components, that need to be understood to solve the problem:

  1. How much time do you have to solve the problem? As described above.
  2. Who has the advantage? In other words, who is in position to do the most damage, assuming there are no impediments to continuous attack from both sides?
  3. Who is in control of the movement or balance of the position? Are you in a position to control their balance or restrict their movement? For example, even if your opponent is on top, where they have the positional advantage, if you are in a position to sweep or reverse them you may have more control of the movement than your opponent.
  4. Is your opponent solving the problem you have posed them? Turn the tables. Just as you are trying to confound their attempts to better you, they are doing the same to you. For example, if you are controlling them in a position of advantage yet they are quickly getting control by setting up an escape, they are solving your problem and will soon be giving you a new problem of your own!
  5. Who has psychological control? This is a key concept that deserves an entire article of its own. We’ll focus on this continually.
  6. What is the physical state of your opponent? Are they injured? Winded? Have you noticed them losing their energy level?
  7. Environmental issues around the fight (walls, chairs, debris, other people – friendly or unfriendly). Many of these can work to your advantage or disadvantage.

Each of these factors needs continuous monitoring for you to understand what the next move is for you in a fight. The more experienced a fighter is, the faster they can assess these factors and act or make corrections to their advantage in a fight. If you sense your opponent is solving the problem, you must change position to create a new problem for your opponent. The faster you change the parameters of the problem, the less likely they will be able to solve this. This creates a huge psychological advantage and accelerates physical exhaustion for your opponent as they struggle to solve these problems. In effect, you are creating an unsolvable problem by changing the problem faster than your opponent can solve it. As we practice flow on the mats, you should concentrate on this concept, since it requires a high level of skill on position transition.

Training for the Unsolvable Problem

Question and Answer

This is a way to take baby steps to “the unsolvable problem.” We break down the rapid-fire problem and response into a slow paced “dialog.” Starting with these positions:

  1. Pass guard
  2. Escape side
  3. Escape mount

…we pose a question in the form of a position, physically asking “How would you escape from this?”

Your partner responds by attempting to escape in one motion. Your partner must resist the compulsion to start fighting your way out. They will make a single move, then let you ask a new question. By allowing them to respond (not resisting the response), you allow the dialog to continue. After they respond, you change your position to present a new problem. And so on…

Rapid Conversation

This is a fast, 3 second exchange of “questions and answers” (a set of 4 or 5 positions flowing into each other as your partner responds). As a quick sequence of questions and answers, it becomes like a very quick match where you stop after 3 seconds and assess your position, awaiting your partner to start another “burst of conversation.” Let the person who started “lead.” Switch lead after a few “conversations.”