9.00 am. Take each hour-pip in turn and note how many other pips are numbered correctly in relation to it.

There are two sets of three pips correctly numbered with respect to each other 1, 4, 9 and 2, 5, 12.
There are four pips, numbered 6, 7, 8, 10 that do not relate to any other pip.
There is only one set of two related pips 3 and 11.

The traveler was told that he could tell the time if he knew how many pips were correctly numbered.
The pips numbered 3 and 11 (a unique set) must be correct otherwise the traveler would have had a number of choices (2 sets of 3 related numbers, and 4 individual numbers)..

Counting counter-clockwise from pip number 11 shows the hour hand pointing to what would normally be 9:00 o'clock, confusingly re-numbered as 2.00 o'clock. The traveler was also told that 12:00 o'clock was no longer at the top of the dial face, so he now knew that the dial face had been rotated 90° counter clockwise.

The traveler met the passer-by in the morning, hence the time is 9.00am.

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