My guess is that they didn't expect you to build a complete system on the white board :D
And giving you a pen tricked your mind into thinking you MUST write something quickly!
They wanted to see how you approach the problem.
The questions you ask about the problem would give them an understanding about whether you can see the different aspects involved with the system.
So next time, think of the Matrix.... "There is no Pen"
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My guess is that they didn't expect you to build a complete system on the white board :D
And giving you a pen tricked your mind into thinking you MUST write something quickly!
They wanted to see how you approach the problem.
The questions you ask about the problem would give them an understanding about whether you can see the different aspects involved with the system.
So next time, think of the Matrix.... "There is no Pen"