This is the problem I came across reading the book The Art and Craft of Problem Solving. When I read this question I wasn't able to figure out the solution and I saw the solution after a while, but still I couldn't understand the solution as well.
Question:
Pat wants to take a $1.5$-meter-long sword onto a train, but the conductor won't allow it as carry-on luggage. And the baggage person won't take any item which greatest dimension exceeds $1$ meter. What should Pat do?
Solution:
This is unsolvable if we limit ourselves to two-dimensional space. Once liberated from Flatland, we get a nice solution : The sword fits into a $1 \times 1 \times 1$ -meter-box, with a long diagonal of $\sqrt{(1^2 + 1^2 + 1^2)}$ = $\sqrt{3} > 1.69$ meters.
Can anyone give me a clear explanation of this solution?