# A mathematical term

Use this to get the answer:

51 12 31 23 22 43 21 52 11 41 32 42

• Hey! Rot13(V'z gelvat gb svther bhg gur cnggrea va gur rknzcyr. Whfg gb pbasvez, gur sbhe-ol-sbhe unf ab pebffrq bhg fdhnerf ba vg, ohg gur guerr-ol-guerr qbrf?) Edit: Never mind, I think I see what I missed. Aug 28, 2021 at 14:04
• Hi, yes that's correct Aug 28, 2021 at 14:44

The top left pretty clearly refers to

KING... As we have the initials of the chess pieces with KING circled.
(Bishop, King, Knight...)

The top right seems likely to be

KNIGHT'S TOUR - NIGHT = K'S TOUR
Putting these together, it seems to indicate that we should be taking a KING on a KING'S TOUR

Except...

The middle icon indicates no diagonal movement.

Sure enough, the "Examples" show valid starting places for an open King's Tour using orthogonal movement of a King on a small chess board. The X's are spaces where no such tour exists.

If we apply that to the given 5x5 grid, every other letter is valid. With the invalid letters colored red, we get:

Note: originally I deleted (x-ed out) the invalid letters. Bad idea! It erased the final answer which you can nearly see here in plain sight!

Now, turning to the numbers:

With 2 digits from 1-5, these seem to be coordinates into the grid. For example, 51 = column(x)=5, row(y)=1, if we use standard indexing. Gives "T".
Continuing with this, we get something like "toets...", but that wouldn't leverage the puzzle. So let's delete out the letters/indexes that we removed from the grid, using only coordinates that were valid for a King's Tour.
We get "51-T 12 31-E 23 22-S 43 21 52 11-L 41 32 42-I" This looks like "TESLI", which isn't a word, but it anagrams to "TILES", but OP has confirmed that is a coincidence, as I suspected (short word with common letters).
So revisiting this with OP's hint in mind that we are looking for a 12 letter word, something I'd noticed earlier was that 12 letters were 'struck out', so perhaps we can use the numbers to spell something with them!
I'd tried originally using them as various index schemes or rot-n schemes on both the red and green letters to no luck (apart from tesli), so credit to @LukasRotter for cracking this overnight.
If we take the first number as the row index (y), and the second number as the column index with the green/valid squares removed (x), we have a 5x3 coordinate system into the grid.
51 is now row 1, column 2 (first red square), giving "O".
Continuing in this manner reveals a mathematical term quite relevant to the puzzle:
ORTHOGANALLY!

One final note:
This was a good puzzle! It took me awhile to figure out BKKPQR. I'd tried googling it to no avail. Could something this creative yet logical really be an original creation??? I still cannot believe there are no online hits to such a logical encoding. I only figured it out when I started looking for connections to the rest of the rebus, and tied it to the picture to its right.

• You're right about the first part! rot13(Gur yrggref bs gur nafjre vf ba gur K'f. Naq gur gjryir gjb-qvtvg ahzoref ercerfrag n gjryir-yrggre jbeq.) Aug 29, 2021 at 7:31
• rot13(Vs lbh bayl gnxr gur erq yrggref naq sbyybj gur vafgehpgvbaf (ebj, pbyhza (nf V fnvq, jvgu nyy oynpxf rkpyhqrq)), vg fcryyf BEGUBTBANYYL) Aug 29, 2021 at 15:56
• Thanks! I had even thought Ort* would be a logical answer, but couldn't get it to work out and haven't had a chance to look at this since yesterday... sneaky using a different indexing for rows vs columns. I'll edit your finding in if you don't mind.
– Amoz
Aug 29, 2021 at 17:41