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On my clock's display, the time has just changed to 02:31. How many minutes will it be until all the digits 0, 1, 2, 3 next appear together again?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

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This problem is taken from the UKMT Mathematical Challenges.