Here is another challenging problem from the first issue of the 1874 The Analyst, which also appears in Benjamin Wardhaugh’s book.
“3. If a line make an angle of 40° with a fixed plane, and a plane embracing this line be perpendicular to the fixed plane, how many degrees from its first position must the plane embracing the line revolve in order that it may make an angle of 45° with the fixed plane?
—Communicated by Prof. A. Schuyler, Berea, Ohio.”
Part of the challenge is to construct a diagram of the problem. I used techniques for a solution that were barely in use when this problem was posed in 1874. The contrast between then and now is most revealing.
See the Rotating Plane Problem
Here is a fairly straight-forward problem from 500 Mathematical Challenges.
Here is another problem from the 2020 Math Calendar.
The following problem comes from a 1961 exam set collected by Ed Barbeau of the University of Toronto. The discontinued exams (by 2003) were for 5th year Ontario high school students seeking entrance and scholarships for the second year at a university.
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This is another problem from the 2020 Math Calendar.
Here is another problem from the 2020 Math Calendar to stimulate your mind.
This is a delightful and surprising problem from 
If you will pardon the pun, this is a diabolical problem from the collection Five Hundred Mathematical Challenges.
This 2005 four-star problem from Colin Hughes at Maths Challenge is also a bit challenging.
This is another stimulating math problem from Colin Hughes’s Maths Challenge website (mathschallenge.net).