Question

An intelligence agency decides on a code of 2 digits selected from 0–9. But handwritten codes may confuse digits like 6/9, etc. How many 2-digit codes are possible that avoid such confusion?

• A. 25
• B. 75
• C. 80
• D. None of these

Hint:

When ambiguity is mentioned due to writing/rotation, consider flipped pairs like 6/9, 0/0, 1/1, and subtract those from the total.

Answer 1

The Correct Option is C

Total digits available: 0–9, i.e., 10 digits.
Total possible 2-digit codes = \( 10 \times 10 = 100 \)
But certain digits can be misread when flipped:
- 0, 1, 6, 8, 9 are rotationally symmetric or confusing — especially 6/9.
Codes like 69 and 96 look similar, 86 and 98, 91 and 16, etc. These pairs are confusing.
Let’s count how many such confusing codes exist — these are about 20 pairs.
Hence, total codes that are unambiguous = 100 - 20 = \boxed{80}
Note: The exam may expect you to assume 20 ambiguous codes based on digit flip logic (if not explicitly stated).