The answer is 81/9 = 54/6 = 27/3. If u asked me about the cause of that intuition my answer will be "I don't know". Even then I followed it and solved the puzzle easily.
My question is "Is it a good idea to follow such instincts?"
In the book "Blink: The Power of Thinking Without Thinking" author Malcolm Gladwell call such a process as "Intuitive Repulsion". The book is all about snap judgments and the contexts in which it proved useful. The author states that "The decisions made very quickly (snap judgments) are every bit as good as decisions made cautiously and deliberately".
I am not sure about weather we should follow such instincts especially when it comes to testing. If following such instincts ends in uncovering bugs then it proves to be really useful. Because delivering (quality) products in time is the major concerns of all management.
And I believe that concept of "Blink" is a two sided blade. It can prove to be useful in times as well as it can mess up your whole testing activity because we are making decision based on little information. So be careful while making decision on weather to follow or not to follow your instincts.
In the post "Quick Oracle: Blink Testing" James Bach describes about "Blink Testing". It is a testing technique that he found helpful. Blink testing is not about snap decisions but about recognizing patterns automatically. He has specified lot of examples where Blink testing will fit. I too tried "Blink Testing" for checking log files, for testing and comparing web pages (I was working on a project for migrating web pages from .Net to J2EE Technologies). And Blink testing really proved useful. Thank you James.