Is drawing an x with a box around it and 4 semicircles impossible?

Question

My teacher gave this to us as a challenge and I think its impossible, but he says there's only 1 solution.

The rules are:
1) no lifting up pencil
2) no redrawing lines
3) no folding paper
4) 1 pen/pencil
5) no erasing
Did my teacher lie about this drawing being possible within these rules?

Answer 1

Assuming you mean a rectangle whose opposite corners are diagonally connected, with semi-circles on each side of the rectangle, then yes, it's mathematically impossible.



Such a construct would have 4 vertices, each with an degree of 5. Since there are 4 odd vertices, it's impossible to construct a Eulerian path (a trail which visits each edge exactly once).

Answer 2

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Answer 3

Draw a half circle on the left, go up top with your line, go down, then diagonally, then down,then across, to the other half circle, and diagonally again.