raffle tickets have been printed, each with a distinct 5-digit number ranging from to . However, some tickets are ambiguous, depending on the ticket’s orientation. For example, is the ticket below or ? How many of the tickets are ambiguous?
Source: NCTM Mathematics Teacher 2008
Examples of unambiguous numbers
Characteristics of an unambiguous number
1) the third digit remains the same after the rotation:
2) once the first two digits are chosen, there is only one way to choose the last two digits.
How many unambiguous numbers?
How many numbers?
How many ambiguous tickets?