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Figure This!


Complete Solution:

In the 100,000,000 eight-digit serial numbers from 00000000 to 99999999, there are 10,000 that read the same forwards and backwards.

Considering this fact, you might expect 1 in every 10,000 bank notes to be a radar bill.

Since there are eight digits, the serial numbers can range from 00000000 to 99999999. In other words, there are 100,000,000 possible serial numbers.

Think of the eight digits as two groups of four. The last four digits of a radar bill serial number determine the entire number. For example, if the last four digits are 0001, then the entire number must be 10000001.

Since the four digits that determine the radar bill serial number range from 0000 to 9999, there are 10,000 possible radar bill numbers.

Since there are 10,000 possible radar bill numbers out of 100,000,000 serial numbers, you might expect 1 of every 10,000 bills to be a radar bill.

Another way to think about this is to look at the following pattern:

No. of Digits in Bill
No. of Radar Bills
2 10
4 100
6 1000
8 10,000

Following this pattern, there could be 10,000 radar bills that have eight digits.

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