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Begin with a similar, but simpler problem. Suppose there were only two digits in a serial number. In this case, a radar bill would have to have a serial number with two identical digits: 00, 11, 22, 33, 44, and so on.

There are a total of 10 of these serial numbers out of the 100 possible 2-digit numbers. If there were four digits, the serial numbers would range from 0000 to 9999. Think of the four digits as two groups of two. If the last two digits were 01, the number of the radar bill would be 1001. How many radar bills would there be altogether for four-digit serial numbers?

 

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