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Solving difficult binary puzzles

Solving the most difficult binary puzzles sometimes requires quite complex steps. For example, try to determine which number can be entered in the blue cell in the puzzle below.

Binary puzzle

This will certainly not be easy, especially for the novice binary puzzler. We'll explain it step by step.

In the fifth row, two zeros and two ones are missing. Because a maximum of two identical numbers can be placed next to each other, there are four ways to complete the fifth row:

Binary puzzle

Binary puzzle

Binary puzzle

Binary puzzle

Since the second option above is the same as the second row of the puzzle, this option is eliminated. Each row must be unique. This leaves three possibilities for completing the fifth row:

Binary puzzle

Binary puzzle

Binary puzzle

By now, it's probably clear which number can be entered in the blue cell. Whichever of the three options we choose, a one will always appear in the fourth position. So, a one can be entered in the blue cell in the binary puzzle.

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