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Slippy Numbers

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.

Find slippy numbers ending in 4 (a small one) and in 2 and 3 (larger ones).

Explain why the slippy number ending in 9 has a unique sequence of digits; can there be more than one slippy number ending in 9?

You might like to write a short program to find other slippy numbers.