A watch reads 3:30. If the minute hand points towards the north-east direction, then in what direction will the hour hand point?

Let's first determine the standard positions of the hands at 3:30 on a normal clock face:
At 3:30, the minute hand points exactly at 6 (which is South in the standard orientation).

The hour hand is exactly halfway between 3 and 4 (which is South-East in the standard orientation).

Now, according to the problem, the orientation is rotated:

The standard South (minute hand direction) is now called North-East.

Let's find the angular shift:

Moving from South to North-East clockwise is a rotation of 225
∘
(or 135
∘
counter-clockwise).

Let's apply the exact same transformation to the hour hand position (Standard South-East):

Standard South-East is 45
∘
clockwise from South.

Since South shifts to North-East, the hour hand will be 45
∘
clockwise from North-East.

45
∘
clockwise from North-East is East.

Let's re-verify alternative simple orientation mapping:

If Minute hand (at 6 o'clock) = North-East

Moving backwards counter-clockwise on the clock face:

4:30 position would be towards North.

3:30 position (hour hand position between 3 and 4) is 75
∘
counter-clockwise from the minute hand.

Let's subtract 75
∘
counter-clockwise from North-East direction:

45
∘
counter-clockwise from North-East is North.

Another 30
∘
counter-clockwise brings us to North-West.

Therefore, the hour hand points in the North-West direction.