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Common Wisdom:

No, you cannot. This is because of a theorem by Leonhard Euler in the field of Graph Theory. I will state this in Graph Theory terms: you cannot find an Eulerian circuit in a graph where more than two vertices have an odd degree. The "y" shape creates three vertices that have an odd degree, thus this is impossible. Please see the link about the Euler path for details.

An alternative view of the question (and answer):

You are thinking inside the box. You are being trapped by constraints which you are assuming, but are not stated in the problem. Of course you can draw a "Y" without picking up the pen or overlapping the lines. Simply draw a "block" letter Y. See the "Y in a rectangle" page for an example. (And, I fail to see how a rectangle makes this problem more difficult.)

Note the elements that make the second answer feasible:

# Interpreting "draw a y" as a "block letter y".

# Interpreting the words "in a rectangle" as meaning that you do not have to draw the rectangle.

I think this is counter-intuitive, but intuition is a subjective thing. Both answers are valuable.

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16y ago

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