I don't know
how the master clock, with which other clocks in the world are synchronized, is setup.
who decided the mechanism used to setup the master clock
when the master clock was setup
how to restore the master clock in case all clocks in the world have been scrambled accidentally.
Therefore, let us keep one clock (that has been previously synchronized with the master clock) in a secret place and scramble all other existing ones and destroy all historical data documented based on these clocks.
How to setup a clock that is in sync with the hidden clock's date plus time?
There is no trap in this question.
You cannot take the hidden clock and use it to synchronize the clock in question. You can make use of the hidden clock only after you have finished setting the clock in question. It means that the hidden clock is available only for comparison.
Any historical data (including calendars, diaries, BIOS, etc) created based on the previous clocks are destroyed.
The hidden clock is the most accurate clock that is identical to an atomic clock.
The scrambled clocks do not show the correct time as the hidden clock shows.