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.

74? I haven't thought it through yet, but it seems that for every 10 2-digit numbers (10-19, 20-29, etc) which start with 1,6, 8, or 9, there are 4 invalid codes (inverting 10, 60, 80, and 90 is not possible because they cannot be read upside down as a valid code) which gives us 16 invalid codes... Subtract 16 from 90 and you get 74 valid codes...

Posted by sean on 2005-08-29 01:37:51