How many ways can you solve a 32-tile word puzzle?

A word changes the next board

Wordchute starts with 32 letters in four columns of eight. The bottom 16 form the playable 4×4 grid. Make a word of at least three letters by connecting touching tiles, including diagonals. Those tiles disappear, and the remaining letters fall straight down in their columns. Empty all four columns and you have a full clear.

All the waiting letters are visible. There is no hidden refill. Boggle-style word finding meets Tetris-style preview planning, with the entire supply in view: which word leaves useful connections after the drop?

This is an expired board, Drop #1 from August 27, 2026. The count below starts after playing SHOW as well. The strategy guide works through choices and their consequences.

First, define “a different solution”

Counting solutions sounds straightforward until two moves spell the same word through different copies of a letter. Or two different words remove exactly the same set of tiles. The next position can be identical even though the input was different.

For a reproducible lower bound on Drop #1, I fixed the first two moves: MIX straight up the first column, then SHOW through the exposed S and H and the bottom-row O and W. That removes seven tiles. I counted every full-clear continuation from the remaining 25 using Wordchute’s wordchute-en-v5 dictionary.

These are exact continuation counts under three definitions. Each is also a lower bound on the number of complete routes through the original 32-tile board, because every continuation can follow those same two moves:

All three counts require dictionary-valid words of at least three letters. Longer words are included whenever their paths fit the playable grid; there is no three-letter maximum. “Remaining-tile routes” merges equivalent tile removals only after finding legal words.

Remaining-tile routes

939,874,993

Count each sequence of remaining tile identities once. Different words or paths that remove the same tiles at a step are merged.

Word-and-tile routes

4,563,697,541

Distinguish the word and the set of tiles removed at each step. Different finger paths spelling that word on that same set are merged.

Exact-path routes

6,917,167,611

Distinguish every ordered finger path at every step, including alternative paths through the same letters.

The original opening has 148 legal word-and-tile choices, producing 126 distinct remaining-tile states. The counts above cover only the fixed MIX → SHOW start, not every opening. No unfinished whole-board search is included in these totals.

These counts include accepted words a person might never think to play. They describe one particular board, and they change with the dictionary. They do not measure how many routes players have discovered.

Download the measured counts and methodology, including the past-board letters, fixed opening paths, counting definitions and source fingerprints. No current or future daily board is included.

The archived counter source records the exact implementation used. It expects repository-local dictionary and board files; the download above identifies the inputs and counting scope.

A small board becomes a state graph

Give each of the original 32 tiles a bit. A 32-bit mask records which tiles remain. Because letters stay in their original columns and keep their relative order, that mask determines the entire position after gravity. The bottom four remaining letters of each column are playable.

There are 2³² possible masks: 4,294,967,296. That is a loose upper bound on tile-subset states, not a solution count. The visible chute gives us a much tighter bound before we even inspect the letters.

The queue rules out most tile subsets

Consider one eight-tile column, temporarily ignoring word and path legality. With zero to three tiles left, there are 93 possible subsets: choose zero, one, two or three of the original eight tiles.

With four or more left, choose the four lowest surviving original tiles. Every original tile above the fourth must still be untouched: it could never have entered the playable four rows while those four tiles survived below it. Those four survivors therefore determine the whole column. There are 70 ways to choose them.

That gives 93 + 70 = 163 structurally possible states per column, or 163⁴ = 705,911,761 across four columns. The three-letter word minimum rules out another 152 states: 16 with exactly one tile removed and 136 with exactly two removed.

The final 705,911,609 is still only an upper bound. It does not enforce touching-letter paths or accepted words. The states actually reachable on a particular board can be fewer still. Different routes can converge on the same state and branch again, so winning routes can outnumber states.

At each state, the counter searches touching-letter paths through a dictionary trie. If a prefix appears in no accepted word, that branch stops. A tile cannot be reused within a word. Every legal move removes at least three tiles, so the state graph has no cycles.

That makes memoization useful: once I know how many clears are possible from a state, every route reaching it can reuse the answer. For word-and-tile routes, the core recurrence looks like this:

count(state):
  if state is empty: return 1
  if state is cached: return cache[state]

  total = 0
  for move in uniqueWordAndTileMoves(state):
    next = state without move.tiles
    total += count(next)

  cache[state] = total
  return total

The other definitions change the accounting. Remaining-tile routes merge moves with the same next mask. Exact-path routes multiply each continuation count by the number of paths spelling that move on those tiles. The counter uses BigInt arithmetic so large totals stay exact.

The completed continuation search visited 2,748,184 distinct nonempty states, including dead ends. It counted continuations rather than storing every complete route. It runs offline; exhaustive counting is not part of a player’s game request.

Build the board backward from a clear

To generate a board, I start with empty columns and a plan for word lengths adding up to 32. The generator chooses words from a curated pool and inserts their letters into touching positions. Those insertions push existing letters up within their columns.

Each insertion records a move that would undo it. Reverse the insertion order and you have a witness: a sequence of legal words that removes every tile. The construction produces a candidate with a known route to an empty chute.

The forward solver then searches for alternatives, and the stored routes are replayed to check spelling, dictionary acceptance, adjacency, playable rows, gravity and complete clearance. The daily schedule stores at least three verified full-clear routes per board.

That production check stops after finding enough routes; it does not enumerate the entire solution space. The exhaustive counter above is a separate tool. A handful of verified witnesses proves solvability, while an exact continuation count answers a different question.

A solver doesn’t tell me how a person will play

A board can have many successful continuations that start with a word I would never notice. It can also offer familiar, tempting words that lead toward an awkward finish. Counting clears does not account for which branches a player is likely to choose.

The first simulation baseline chooses uniformly from legal dictionary moves. That is useful as a machine baseline, but it treats an obscure word as just as likely as an obvious one. Generator search effort has a similar limitation: the machine’s workload is not a measure of human difficulty.

The newer model uses three seeded policies. A novice policy favors familiar three-to-five-letter words and simpler paths. A regular policy accepts broader vocabulary and considers board mobility. A strategic policy gives more weight to longer words and familiar follow-up moves.

“Familiar” is still a proxy. It comes from curated vocabulary represented in stored solution routes, inflections and word length, rather than a measured English frequency corpus. Changing those stored words can change predictions across the inventory. We therefore analyze the final inventory together under the same model.

For the October 2026 calibration, we ran 5,000 of these simulations per board: 2,000 novice, 2,000 regular and 1,000 strategic. We also checked whether plausible openings had a known or sampled clear continuation, how accessible the stored routes were, and how often simulated runs ended with one or two tiles.

That last measure matters because words require at least three letters. One or two tiles left cannot form a valid word. Clearing nearly everything can still leave an unsolvable ending, so the quality of a finish deserves attention alongside total progress.

Check the model against actual play

In an early September 1–9, 2026 comparison, we grouped 158 player-board pairs by simulated clear rate. A player who played several boards contributes several pairs, so this is not a sample of 158 independent people.

The direction was encouraging, but this was a small observational comparison. The simulated rates used the familiarity vocabulary from before a later schedule update. It is evidence to refine a scheduling heuristic, not a validated predictor of anyone’s chances.

An earlier blended score could label a board “Easy” even at a 1% simulated clear rate. The internal challenge score now follows simulated clear rate more directly. We still examine vocabulary, plausible openings and last-mile traps separately, and keep the model’s estimates distinct from observed player outcomes.

What I want from a daily board

I wanted a puzzle where every letter was visible and the starting position could always be completed. Building it led to several separate engineering questions: can it be cleared, how many routes clear it, which choices seem plausible, and how does it actually feel to play?

The backward generator answers the first question. The counter explores the second. Simulations help screen the third. The fourth still needs people.

What keeps the game interesting to me is that the same 32 letters leave room for different ways of thinking. You can see what falls next, but you still have to choose which future board you want to create.

More about Wordchute

• Why I built Wordchute

  From Boggle-style word finding to Tetris-style preview planning: why Colin Hanson built Wordchute, a daily word puzzle with all 32 letters visible.

• How to plan a full clear

  Learn Wordchute strategy with worked board examples: predict letter drops, choose word order, avoid stranded tiles and plan a route to clear all 32 letters.

• A full-clear walkthrough

  Follow an illustrative Wordchute board from 32 letters to a full clear. Learn to read the chute, preserve useful vowels and avoid stranded tiles.

Practice on past boards. Today and three recent past boards are free. Older boards are available in the app.