# What is the longest word contained in this new puzzle?

I created a word puzzle:

Here is the puzzle:

Here are the rules:

1. The goal is to spell the longest word possible.
2. To do so, you must place three different color arrows anywhere on the board. You must place one Red arrow, one Green arrow, and one Blue arrow
3. You can place the arrow in any orientation (up, down, left, right, and any diagonal)
4. The way word generation occurs is in the following manner. Whatever letter an arrow sits on top of will be pushed to a stack of letters in an iterative fashion, starting first with the letter the red arrow sits on top of, followed by the green arrow, followed by the blue arrow (R --> G --> B). After one “round” of iteration has occurred, identify the next letter that the red arrow points to and put that letter to the stack. Do the same for the green arrow, and then for the blue arrow. Continue this process indefinitely.
5. The board loops around Pac-man style, such that if you have reached the edge of the board, the next letter in the sequence is the letter on the opposite side of board. So if you have an arrow pointing UP on the top left "R", the next letter it would go to is the letter "E" (at the bottom of the board). If a North-East arrow is on the letter "G" in the example above, the next letter is a 'C.'
6. If, in a given round of moves, there is a collision between two adjacent color arrows (e.g. a collision between where the Red arrow is going and the Green arrow is going, or where the Green arrow is going and the Blue arrow is going), the letter that gets put on the stack is a letter of your choosing.
7. You can put two arrows on the same starting letter, but they cannot be in the same orientation
8. The word that you construct does not need to appear at the beginning of the stack. The word letter sequence SEBOATS can be produced from the puzzle above, which would get you the word "Boats."
9. If all three arrows were pointing at the same square, you get to choose 2 wildcards which would consume all three turns

Example:

• I have placed a red arrow on T, a blue arrow on R, and a green arrow on H. Therefore the first three letters pushed to the stack in the first round are: THR

• In the second round, the next letter pointed to by the red arrow is the letter “E”, which gets pushed to the stack: THRE

• However, there is a collision between the blue and the green arrows. Because of this, I can choose any letter of my choosing to replace the letter “O.” This decision takes up the letter used by both arrows. In this case, I choose the letter “E.”

• As a result, I have spelled the word “THREE” and would earn five points.

What is the longest word you can find inside? Checkmark will be awarded to the individual who can find the longest word.

Edit: Because there seems to be some confusion about how looping around the board works when you use diagonal arrows, here's a diagram for how it would work for South-West diagonals. Each color arrow line represents the axis around which an arrow placed in one of those squares would loop. An arrow South-West or North-East on either the top-left 'R' or the bottom-right 'D' would generate "R" and "D" indefinitely. A south-west arrow placed on "G" would yield: G --> I --> N --> C --> G --> I --> N --> C, indefinitely.

• @APrough, only that first round. After that they'd be pointing to different places. See rule 7. May 14, 2020 at 15:44
• As I mentioned, any word contained in the Enable word list I linked to is fine. Phrases aren't words and neither are abbreviations. For hyphenated words, let's say that those are fine, but it would require that you make a collision and use as your collision letter a hyphen. May 14, 2020 at 17:17
• @FreddyFlares I just added a visual that hopefully clears it up. I see now why it was confusing to people. I hadn't even considered that as a possible interpretation. May 14, 2020 at 21:42
• How would rule 6 work if all three arrows were pointing at the same square? Would I get to choose 2 wildcards which would consume all three turns? Or would I get to choose a single wildcard which would consume the red and green turns, with the blue arrow giving the letter on which it sits next? May 17, 2020 at 12:16
• You get to choose 2 wildcards that would consume all three turns. @cyberpotato May 17, 2020 at 15:56

The longest words I could find were 13 letters long:

disincentives, expectorating, expectoration, liberalnesses, literalnesses, mastigophoran, nonconfidence, seismometries, superannuated, superannuates, tensiometries

For example, the first one can be found as follows:

The red and green arrows start by colliding, so we push a D to the stack, which is followed by the blue arrow pushing an I to the stack. We now have all three arrows pointing at the same square, so we can push any two letters to the stack. In this case, we push SI. Now the red and green arrows continue to collide while the blue arrow loops around the board, and after a couple of rounds we obtain DISINCENTI on the stack. Once again, all three arrows point at the same letter, so we can push VE to the stack. We finish by pushing S to the stack due to the collision between the red and green arrows, and hence obtain DISINCENTIVES.

This method generates a large quantity of collisions (here 9 out of the 13 letters are formed by collisions), by placing two of the arrows on the same square but in opposite directions. This respects rule 7, but allows us to generate at least one collision every round by exploiting the wrap-around mechanic.

As this feels a bit exploitative of the rules, I have also looked for the longest words which do not use this method. The longest words I could find were then 11 letters long:

irritations, observances

Once again, the first one can be found as follows:

In this case, following the rules layed out, and pushing the correct letters from the collisions, we obtain TIIRRITATIONS, which gives IRRITATIONS when ignoring the first two letters. Here, only four out of the eleven letters are generated by collisions.

Finally, the longest words I could find which do not use any collisions were 8 letters long:

andesite, baronies, baronnes, daphnias, enfacing, enlacing, fantasia, inducing, lamberts, muricate, pulicide, reorders, rigaudon, rottener, studdies

The first one can be obtained as follows:

• Wow, this is absolutely incredible. Amazing work. I was hoping somebody would notice the exploitative collision rule you identified -- so kudos to you. Also very impressed you managed to find such long words with no collisions at all. May 18, 2020 at 15:40
• If you don't mind me asking -- how did you discover some of these words? I imagine mastigophoran isn't part of your normal vocabulary :-p I don't mind computer solutions May 18, 2020 at 16:10
• Indeed it isn't, I'd never heard of it before! To answer your question, I simply generated all of the sequences which could be obtained from the grid, then cross-referenced it with the Enable word list you linked. It seems like that list was quite extensive, considering some of the solutions I found! May 18, 2020 at 19:28