An intellingence agency wants to have codes. For this it uses two digit natural numbers such that the two digits are different. Each of these codes are written on different sheets of paper so as to be used. However, the director of the agency soon realizes that many codes are not uniquely recognisable.
For example, 61 and 19 is one such pair because when the sheet of paper is read upside down, a different number may be read. However, 01 is invalid (no leading zeroes).
How many useful codes are there that the agency can use?
Note: The only digits that make sense when inverted are 0,1,6,8 and 9.
Total valid codes = 69
As total numbers from 10 - 99 = 90
Invalid codes:
1. Having both digits same = 9 (11,22,..,99)
2. Reversible numbers with digits 1, 6, 8, 9. = 12
Thus total valid codes = 90 - (9+12) = 69
Solution
