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.

I believe there should be 45 usable numbers. There are 99 numbers from 01 to 99. However, the following numbers are invalid for the reasons stated above.

01,02,03,04,05,06,07,08,09 <9>
10,11,16,18,19 <5>
20,21,22,26,28 <5>
30,31,33,36,38 <5>
40,41,44,46,48 <5>
50,51,55,56,58 <5>
60,61,66,68,69 <5>
70,71,76,77,79 <5>
80,81,86,88,89 <5>
90,91,96,98,99 <5>

Posted by Jeff on 2005-05-12 20:06:11