Find the pattern of matrices

fill the matrix correctly and the guess the Letter and number of 5th matrix:

PS: I'm sure you won't need options!

• For each black square, count the row number and add them all up. SUM = number part. now count the column number for each black square. With a sum 'x', find the x'th letter of the alphabet. As for the pattern, it should have 6 blocks (2/3/4/5/6 sequence). I'm not clear yet on how the pattern actually continues, besides noticing each square seems to shift one step in ever next grid. Guess I should be able to deduct 'direction of movement' for every new element as well as 'point of origin'. Sep 5, 2014 at 22:16
• My attempt to track the movement of the blocks so far: i.imgur.com/OstaRHC.jpg , can't see how to predict where the new block 'F' should emerge. Thererfor, just comments and no answer yet. Sep 5, 2014 at 22:34
• @TimCouwelier you are so close to answer!
– Rafe
Sep 6, 2014 at 4:41
• 'Close' won't do it for an answer though. When my head clears up a little I might try and finish. Sep 6, 2014 at 7:17

| |X| | | |
|X| | |X| |
| |X| | | |
| | |X| | |
| | |X| | |
O + 17


The first piece moves to the right, the second moves down, the third moves left, the fourth moves up, and so the fifth probably moves right.

The letters and numbers are the sum of X and Y coordinates respectively, with the upper left corner being coordinate $(1,1)$ or $(A,1)$.

Each image introduce its new element at the position given by the coordinate sum of the previous image.

Both movement and new positions wrap around, so when a piece would move over the border it appears next to the opposite border, similarly a piece that appear at for instance $(H,11)=(8,11)$, will wrap around to $(8\mod5,11\mod5)=(3,1)=(C,1)$.

• Well done, That's right!
– Rafe
Sep 6, 2014 at 10:12
• figured I needed to test that myself.. came here, saw you did it. :) Sep 7, 2014 at 14:25
• @TimCouwelier Posting partial solutions is dangerous. Here, have an upvote for your magic sudoku as thanks for your help. Sep 7, 2014 at 18:10
• @eBusiness: By all means, I'm glad someone picked up the hints and got a full answer. I'm not deliberatly looking 'to take credit'. If I can't answer in full, I'll gladly put whatever I can answer in comments. (If I'd perceive this as competition rather then 'fun' - I shouldn't be here to begin with) Sep 8, 2014 at 8:26
• @TimCouwelier I principally agree, I just can't help being a little competitively minded at times. Sep 8, 2014 at 14:52