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Logic Equations 5x5 - #21

In this 5x5 Logic Equations you have to find unique integer values for the variables (ranging from 1 to 5) to make all statements true.

How to play

  • The variables represents unique integers ranging from 1 to the number of variables;
  • Multiplication is implicit: AB means A times B, or A * B;
  • Based on the clues (equations and inequations), use the grid to create relations between variables and values:
    • Click once on a square to mark that value as false;
    • Click twice to assign the chosen value to the variable;
    • Click three times to clear the square.
  • The color of a clue changes after you assign values to all of its variables:
    • GREEN means that the statement is true;
    • RED means that the statement is false.
  • Click on a clue to mark it as used;
  • The game ends when all values are correctly assigned to the variables.

Tips

  • Figuring out which variables can't have the lowest or the highest values is a good starting point, e.g, A > B shows that A ≠ 1;
  • Analyzing the hypothetical equation C + D = 4, we can make the following statements:
  • Another quick tip: A = 2B means that A is even;
  • Don't be afraid of using pen and paper. Some puzzles might require it.

More 5x5 puzzles

  • A + B ≤ 7 if and only if C < 1
  • A + C ≤ 7 if and only if D + E ≤ 8
  • A + E ≤ 7 if and only if C + D ≤ 4
  • E > 2 if and only if C ≥ 2
  • E ≤ 4 if and only if C + D ≤ 3
  • A + D ≤ 4 if and only if B + E ≤ 4

Solve

  • D + E = A
  • 2E = B
  • 2B = A

Solve

  • D = BB
  • AD = D
  • E > 3

Solve

Strategies for Solving Complex Logic Equations

For tackling complex Logic Equations, a systematic approach is often more effective than random guessing. One strategy is to employ the process of elimination. Start by filling in the most obvious values based on the given clues and then work your way through the less apparent ones. As you assign values to variables, revisit previous clues to see if they offer new insights. This iterative approach can help you uncover relationships between variables that may not have been evident initially.

Another advanced strategy is to use "what-if" scenarios. When you encounter a grid that has multiple plausible solutions, pick a variable and temporarily assign it a value. Then, proceed to solve the rest of the puzzle based on this assumption. If you reach a contradiction, you know that the initial assumption was incorrect, and you can backtrack effectively. This technique, often referred to as "hypothetical reasoning," can be particularly useful for breaking through challenging sections of a puzzle and can save you a lot of time compared to brute-force methods.

Training your Brain with Logic Equations

Playing Logic Equations is not just a fun pastime; it's also an effective way to train your brain. The game challenges various cognitive skills, including problem-solving, logical reasoning, and pattern recognition. As you work through each puzzle, you're essentially giving your brain a workout, much like how physical exercise strengthens muscles. The more you play, the better you become at identifying relationships between variables and clues, which in turn improves your overall cognitive abilities.

Moreover, Logic Equations can also help enhance your focus and concentration. The game requires a high level of attention to detail, as even a single mistake can lead you down the wrong path. This level of engagement helps to improve your ability to concentrate on tasks for extended periods. Additionally, the game's iterative nature encourages a growth mindset, teaching you to learn from errors and adapt your strategies. Over time, these benefits can extend beyond the game, positively impacting other areas of your life that require logical thinking and sustained attention.

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