# The Vibrant Periodical

The image below will allow you to find a nine-letter word that describes the nature of this puzzle. Good luck! Text Version:

N P R Y O Y K K R       Y K P S R S B B N
R N L O S S B N O       P K S R K K W S Y
O K N Y G O G S R       G S Y S B L K P L
Y O L N K B N O B       N S K P N L S Y W
B L O O L O Y R P   +   G G P P S L G Y W
G S P O B O K B K       R R S N R N G P G
Y B P Y P P G G N       K S L B B G P W W
O K S R P B B G B       W L R W B N Y W Y
B P B P S B S N O       S Y P B P R L W B

R: Red         B: Blue
O: Orange      N: Navy
Y: Yellow      P: Purple
L: Lime Green  K: Pink
G: Green       W: Brown
S: Sky Blue


Note: Neither the names I have given the colors nor the letters used to represent them are used to solve the puzzle.

Hint:

Hint 2:

There are more mathematical concepts involved that you might first expect.

Hint 3:

If at first you don't succeed, try, try again.

Hint 4:

Each color brings something useful to the puzzle. Though not necessarily all at the same time.

• Do you have a text version of the two grids (say, using a different letter for each color)?
– Deusovi
Nov 29, 2022 at 18:11
• I will happily make one. Thanks for the suggestion. Nov 29, 2022 at 18:12
• Welp, pretty sure I know the final answer via the hint, but not how to exactly get to it :) Dec 1, 2022 at 10:30
• Pretty sure I figured out how to use the hint (and how to get to it), but I'm not sure how to get to the final answer after that! :) Dec 2, 2022 at 8:52
• For reference: pastebin.com/jEUqMAkf. Only thing I see immediately is that the Ws of A+B+A look like an S Dec 7, 2022 at 8:50

The nine-letter word is

Recursive

Explanation

As per hint #1, adding two grids together means adding the numeric values of the two cells (given by the color strip), dividing it by 11 (= number of colors) and taking the remainder as the result.  The arrow in the image suggests we need to do something further with the result of adding both grids together. At first I thought A-1 means "inverse of grid", but with hints #3 and #4 it became clear that this actually hints towards a sequence! I.e. "Sequence A index -1".

So if we just keep on adding the first grid to the result of our previous calculation, we can see something peculiar on our first try: Looks like the brown cells form the shape of the letter S, which yields the first actual letter of the sequence! Let's do it 10 more times to cover all colors, i.e. keep on adding the first grid to our current result:          This gives us two invalid shapes (for Y/O's turn), so ignore those. The rest gives us suceevirr, which is an anagram of the answer, RECURSIVE.

• Wonderful job. Congratulations on the solve. Dec 7, 2022 at 16:40
• Additional Note: rot13(Vs lbh erphefviryl nqq gur Frpbaq tevq, vg fcryyf gur jbeq erphefvir va beqre bs pbybe.) Dec 7, 2022 at 16:43