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

**SOLUTION**

Examples of unambiguous numbers

Characteristics of an unambiguousÂ 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?

**Answer**:

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