Picture the scene, of sitting bored in your university/college common room, or "JCR" as they are known in these parts, in the void period between two supervisions, or tutorials as they would be known over at That Other Place. Your preparation work for the second is complete, and the JCR/location of second supervision is too far from halls of residence to feasibly head back and doss for a brief period in between. Luckily, you spy an untarnished back page of The Times 2, and hit the Sudoku puzzles...

Now, bring in the other consideration: your first supervision/tutorial of the two had been on the Eigenvalues & Eigenvectors elements of Matrices Mathematics, so certain items are whizzing around your head...

What is the resultant of the Venn diagram-like intersection of these two conditions? Why, the answer is simple of course! You've only just thought of one of the most sick and twisted-minded method to set some advanced mathematics exam questions...

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1) Attached to your question paper is the back page of tomorrow's Times2. Choosing any two of the Sudoku grids given on this page, produce the completed grid for both of your choices, ensuring you follow the common rules: integers 1 to 9 in all nine rows, columns and boxes, once and only once, ensuring there are no clashes.

More maximum marks are available to those opting to solve the Killer Sudoku puzzle as one of their two choices, and less marks are attainable if you go for the noddy-maths "Easy" difficulty grid.

We give you tomorrow's copy to ensure those of you who do these Sudoku pages daily would have no advantage by knowing the answers. It's not fair to just memorise the 9x9 grid now is it?

Please ensure that you indicate on your answers paper which two Sudoku grids were attempted.

2) The perceptive among you will note that your two solved Sudoku grids form a pair of 9x9 matrices. Denoting one of your grids as Matrix A and the other as Matrix B, solve:

a) 9x9 matrix multiplication of A B

b) Calculate the eigenvalues and eigenvectors for both matrices A & B

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I wouldn't say this question would be insolvable at all, but, I dunno, the perfect collision of heavy-duty mathematics with a modern-day pastime of logic and deduction would make for a rather hilariously synoptic final exam question. I'm also sure 2(c) could be developed, as could q3 etc... The exam paper suggested above is hardly exhaustive.

So yes, go find a mathmo' and tell him (or her) to have fun with this geezer! I suppose it's not simply the mathematicians who would embrace this jocularity, NatSci's, Engineers, CompSci's too I suppose. It would be a bitch of a paper for whoever's marking them though, haha.

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