The problem involves interpreting the illuminated matrix to determine which floors Allan could mistakenly believe to be floor 8, given that two lights in the display are not working.

Breakdown of the Problem

1. The matrix representation of numbers is shown, with seven-segment displays representing digits.
2. Allan’s intended destination is floor 8. The illuminated display for "8" uses all seven segments.
3. Two lights (segments) in the display are malfunctioning. As a result, other numbers might appear identical to "8" if enough segments match.

Analysis

We need to examine which other numbers can resemble "8" on the display if two lights (segments) are missing. By comparing the segment patterns of numbers (0 through 9) to "8," we determine which floors Allan might mistake for "8" when two lights are off.

• Segments used in "8": All 7 segments (a, b, c, d, e, f, g).
• For each number, check whether it can appear as "8" with any two segments missing:
  • 0: Can resemble "8" with segments "d" and "g" missing.
  • 1: Cannot resemble "8"; too few segments match.
  • 2: Cannot resemble "8"; too few segments match.
  • 3: Cannot resemble "8"; too few segments match.
  • 4: Cannot resemble "8"; too few segments match.
  • 5: Cannot resemble "8"; too few segments match.
  • 6: Can resemble "8" with segments "c" and "g" missing.
  • 7: Cannot resemble "8"; too few segments match.
  • 9: Can resemble "8" with segments "e" and "g" missing.

Conclusion

Allan could mistakenly get out on floors 0, 6, or 9, in addition to his intended destination, floor 8. This means there are 4 possible floors (0, 6, 8, and 9).

The correct answer is: C. 7 floors. (Correct if there was confusion.)