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.
There are 90 two-digit numbers with no leading zeros (10 - 99).
Out of those, 12 can be flipped to produce a different number:
16 61 81 91
18 68 86 96
19 69 89 98
This leaves 78 two-digit numbers that can be used.
However, 9 of those numbers do not have unique digits:
11
22
33
44
55
66
77
88
99
Excluding those numbers leaves 69 useful codes.
Solution?
