At first, Julian and Kelvin were facing the same direction. Julian then turned $45^\circ$ anti-clockwise while Kelvin turned $135^\circ$ clockwise to face North. What direction did Julian face in the end? Ans: ___

1. Determine the initial direction both were facing by working backwards from Kelvin's final direction.

Kelvin turned $135^\circ$ clockwise to face North.
Working backwards, the initial direction is $135^\circ$ anti-clockwise from North.
$135^\circ = 3 \times 45^\circ$, which is 3 compass points anti-clockwise from North.
North $\rightarrow$ North-West $\rightarrow$ West $\rightarrow$ South-West.
So, both Julian and Kelvin were initially facing South-West.

2. Determine Julian's final direction.

Julian was initially facing South-West.
He turned $45^\circ$ anti-clockwise.
$45^\circ$ anti-clockwise from South-West is South.