Ten-digit numbers

I have a calculator that can display ten digits. How many different ten-digit numbers can I type using just the 0-9 keys once each, and moving from one keypress to the next using the knight’s move in chess? (In chess, the knight move in an L-shape-one square up and two across, two squares down and one across, two squares up and one across, and other like combinations.)

REVEAL THE ANSWER

You can form the numbers 5034927618 and 5038167294. You can also form their reverses: 8167294305 and 4927618305. Hence four different numbers can be made.

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