Rotation Is Visual Only

A turned board is the same board

Some boards read better sideways. Maybe you hold your phone at an odd angle on the couch. Maybe a word hides down a column and your eyes are used to reading across. So you look at the letters from a new side, and they land in new places.

A fair question follows. Did that change the puzzle?

It did not. Looking from another side changes the view. It does not change which tiles touch, which words can be traced, or what a word is worth. This note walks through why, and shows it on a small made-up grid so you can check every step yourself.

What a turn can and cannot change

A turn moves every tile together. Picture a paper grid on a table. You spin the paper a quarter turn and every letter goes along with it. Neighbors stay neighbors, because nobody tore the paper.

That is the whole idea. The letters keep their company. The tile that sat beside the E still sits beside the E. Two tiles that met at a corner still meet at a corner. Only the words you use to describe the spot change. What used to be "to the right" may now be "below."

So we say rotation is visual only. This note treats a turn as a way of looking, the same as tilting your head or holding a printed board upside down. You are choosing a comfier angle for your eyes. You are not getting a different puzzle, and you are not getting an easier or harder one.

We are also not describing any button or control here. This is about the view, and the view is all that changes.

The rules that stay put

Pathwords at pathwords.co has a small set of rules, and a board seen from any side follows every one of them.

• Every word is one connected trail.
• Each step goes to a touching tile in any of eight directions: up, down, left, right, and the four diagonals. Sides and corners both count.
• Inside one word, a tile is used once. Across different words, tiles are free again.
• A word needs at least 3 letters on Mini (3x3), and at least 4 letters on Classic (4x4) and Mega (5x5).

None of those depend on which way the board faces. "Touching" is a fact about the grid. It has nothing to do with the screen.

Scoring stays put too. Listed words pay 2 points a letter and are the only words that move your rank through Start, Good, Great, Awesome, and Genius, where Genius is 100% of the listed maximum. Bonus words pay 1 point a letter in their own pot, count toward the fifth star, and never move Genius. A word is listed or bonus whether you read it left to right or top to bottom.

Hints stay put as well. You get three per puzzle per mode, and a different viewing angle does not add one or take one away.

A made-up Classic board

Here is a board we invented for this note. It is a made-up Classic 4x4. It is not a live daily and will not show up as today's puzzle.

Original orientation:

P  L  A  N
S  T  E  R
O  R  I  D
W  E  N  T

Rows run 1 to 4 from the top, and columns 1 to 4 from the left. So the P is row 1, column 1 (written r1c1), and the last T is r4c4.

Now the same made-up board turned 90 degrees clockwise. The old bottom row becomes the left column, read from the top down. The old left column becomes the top row, read from the bottom up. We built this with a short script instead of by eye, so the letters are right.

W  O  S  P
E  R  T  L
N  I  E  A
T  D  R  N

Look at the corners. P was top left and is now top right. W was bottom left and is now top left. Same tiles, new seats.

If you want to check it by hand, take the old left column from the bottom up: W, O, S, P. That is the new top row. Take the old second column from the bottom up: E, R, T, L. That is the new second row. The other two rows follow the same way.

One word, two views

Take PLAN. On the original board it runs along the top row: r1c1 P, r1c2 L, r1c3 A, r1c4 N. Four tiles, each touching the next, all in a line.

On the turned board, the same four tiles sit down the right edge: r1c4 P, r2c4 L, r3c4 A, r4c4 N. It is the same trail. The word that ran left to right now runs top to bottom.

Here is a trickier one. LATE has a diagonal step in it.

• Original: L at r1c2, A at r1c3, T at r2c2, E at r2c3.
• Turned: L at r2c4, A at r3c4, T at r2c3, E at r3c3.

The step from A to T is a corner step both times. In the original, A is above and to the right of T. In the turned view, A sits below and to the right of T. The direction words changed, but the two tiles still share a corner, so the step still counts.

The words we checked

We checked seven words on both boards with a small program. For each word it found a legal trail on the original grid and mapped every tile to its new seat after the turn. Then it confirmed the mapped trail is legal on the turned grid, with the same letters in the same order and no tile used twice. It also searched the turned grid on its own and found each word there.

Coordinates are row and column, counted from 1.

All seven passed. For a clockwise quarter turn on a 4x4 board, a tile at row r, column c moves to row c, column 5 minus r. That one rule did all the mapping. Try it on the last tile of TEAR. The R at r2c4 goes to row 4, column 5 minus 2, which is r4c3. That matches the table.

Whether a word is listed is a separate question from whether it can be traced, and the angle you look from does not touch either one.

A diagonal stays a diagonal

Now the part that sometimes worries people: corners.

On the original board, the T at r2c2 and the I at r3c3 touch at a corner. After the turn, the T is at r2c3 and the I is at r3c2. They still touch at a corner, only the corner leans the other way. One used to slope down and to the right. The other now slopes down and to the left.

We checked this more widely too. A 4x4 board has 42 pairs of touching tiles, counting sides and corners. We turned the board, mapped all 42 pairs, and got exactly the same 42 pairs back. No pair was lost and no new one showed up.

That is the quiet fact under everything here. A quarter turn shuffles where tiles sit, but it maps the set of neighbor pairs onto itself. The picture of who touches whom is unchanged. Any trail you could draw before, you can draw after. Any trail you could not draw before, you still cannot.

Same neighbors, shuffled order

You can see the same thing from one tile's point of view. Take the I in the middle of the made-up board. On the original it touches eight tiles: T, E, R, R, D, E, N, T. After the turn the I has moved to r3c2, and it still touches eight tiles. Read them off and you get E, R, T, N, E, T, D, R. Sort both lists and they match letter for letter: D, E, E, N, R, R, T, T.

The order you meet them in changed. The company did not.

Edges and corners follow the same logic. On a 4x4 board, a corner tile has 3 neighbors, an edge tile has 5, and a middle tile has 8. Four corners, eight edges and four middles add up to 84 touching ends, and 84 divided by 2 is the 42 pairs we counted. A turn sends corners to corners, edges to edges and middles to middles. A tile never gains a neighbor by changing seats.

Why a word can look harder after a turn

A board seen from a new side can feel different, and that deserves a plain word.

Most of us read in rows. When a word runs along a row, our eyes catch it fast. When it runs down a column, it can hide for a while. Look at the board from the other side and the words that were hiding in columns now sit in rows, while the easy ones stand on end. Nothing was added or removed. Your reading habit is what shifted.

Take WENT on the made-up board. On the original it sits in the bottom row, and most people spot it quickly. On the turned board the same four tiles run down the left edge as W, E, N, T. A reader who scans across may pass right over it. The trail is just as legal. It only asks your eyes to read downward.

RIDE works the other way. On the original it bends around the right side of the middle, and the bend is easy to miss. The turned board lays it out as R, I, D, E over r4c3, r3c2, r4c2, r3c3. That is still a bend. A fresh view just gives you a fresh chance to notice it.

Some players like a new angle for a stubborn stretch. Others never use one. Both are fine. It is a view choice, like holding a book closer to the light.

Reading by letters, not by direction

If you do look at a board from another side mid-search, one habit helps. Stop saying "next it goes right" in your head. Say the letters instead. You are on the T and you want an I. Find an I, then check that it touches the T.

Direction words go stale the moment the view changes. Letters and touching do not. A trail is a chain of letters where each link touches the next, and that sentence is true from every side of the table.

This habit also helps with the diagonal steps people forget. When you hunt for the next letter, scan all eight spots around your current tile, not just the four that point along the lines. The made-up I has eight neighbors and four of them sit on corners.

A second small habit is to name a word's first and last tiles before you trace it. In TIDE the T is at r2c2 and the E ends at r2c3. Those two tiles are neighbors, so the word loops back on itself. Loops like that look odd from one side and obvious from another, which is one more reason a fresh view can be worth a glance.

Words that share tiles, seen from either side

TIDE and RIDE are a nice pair to compare. Both end in IDE, and on the made-up board they share the I, the D and the E. TIDE starts on the T at r2c2. RIDE starts on the R at r2c4. After the turn they still share those three tiles, now at r3c2, r4c2 and r3c3.

That overlap is allowed. Inside one word a tile is used once, and across different words tiles are free again. Finding one word never spends its tiles for the next. A new view does not change that either, so a cluster you found before the turn is still a cluster after it.

TRIED is a good stretch test because it is five letters and it runs through the middle. The trail goes r2c2, r3c2, r3c3, r2c3, r3c4, and no tile repeats. Turn a paper copy and the same five tiles move together. The word is as long and as legal as before.

Progress, the daily, and the rest

Looking at the board from another side does not touch your progress. Progress stays in this browser, and there are no accounts on the web. There is no leaderboard either, so no angle of the board can cost you a place in a line.

The official daily is untimed and rolls over at your local midnight. A board that looks new at ten at night and looks the same at ten the next morning is a new board only because the day changed.

If you like to leave once the list feels done, a different angle is no reason to keep going or to stop. It is just a view.

A note on names

pathwords.co is published by Pathwords. It is not ThinkFun PathWords, it is not pathwords.co.uk, and it is not any of the other lookalike apps that happen to use similar words. If you are ever unsure which one you have open, check the address bar.

Try it on a board that is not made up

If you like, open today's board at pathwords.co. Pick a word you already found and write its trail down in letters and touching tiles. Then look at the board from another side, with your head tilted or your phone held a different way, and read the trail again. You should find the same tiles in the same order, touching in the same ways.

Then go back to the usual view, or stay with the new one, and carry on at your own pace. There is no clock to beat. Leave whenever the sitting feels done.

Published by Pathwords