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'Different Digital Clock' printed from http://nrich.maths.org/
A digital clock uses two digits to display hours, two digits to display minutes and two digits to display seconds, e.g. $10$:$23$:$42$.
How many times between $10$:$00$:$00$ and $11$:$00$:$00$ on the same morning are all six digits different?
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This problem is taken from the UKMT Mathematical Challenges.