Poople #442: FUSS to POOP

Path analysis

This route reaches POOP in 6 moves. Breadth-first search reaches every route with fewer moves first, so POOP cannot be reached in fewer than 6 moves from FUSS.

Moves

6

Difficulty

Hard

Shortest paths

8

The dictionary has 8 equally short routes; the route below is one of them.

1. Move 1: FUSS → CUSS — change the 1st letter from F to C.
2. Move 2: CUSS → CUBS — change the 3rd letter from S to B.
3. Move 3: CUBS → COBS — change the 2nd letter from U to O.
4. Move 4: COBS → COOS — change the 3rd letter from B to O.
5. Move 5: COOS → COOP — change the 4th letter from S to P.
6. Move 6: COOP → POOP — change the 1st letter from C to P.

Computed route analysis

8 equally short ladders connect FUSS to POOP in 6 moves, making this a hard puzzle. The narrowest decision comes in the second half, at BOOS: only 1 of 21 possible one-letter changes from BOOS can keep a shortest route on track. The counts use Poople's accepted word list (2,398 words).

Shortest word ladders

This puzzle has 8 shortest routes. The archive contains 442 puzzles. Showing 8 shortest routes.

1. Route 1: fuss → cuss → cubs → cobs → coos → coop → poop

   1. Move 1: FUSS → CUSS. 9 accepted words are one letter away; 3 of those keep a shortest route (CUSS, MUSS, SUSS).
   2. Move 2: CUSS → CUBS. 12 accepted words are one letter away; 3 of those keep a shortest route (CUBS, CUPS, CUTS).
   3. Move 3: CUBS → COBS. 17 accepted words are one letter away; 1 of those keeps a shortest route (COBS).
   4. Move 4: COBS → COOS. 19 accepted words are one letter away; 1 of those keeps a shortest route (COOS).
   5. Move 5: COOS → COOP. 15 accepted words are one letter away; 1 of those keeps a shortest route (COOP).
   6. Move 6: COOP → POOP. 14 accepted words are one letter away; 1 of those keeps a shortest route (POOP).

2. Route 2: fuss → cuss → cups → cops → coos → coop → poop

   1. Move 1: FUSS → CUSS. 9 accepted words are one letter away; 3 of those keep a shortest route (CUSS, MUSS, SUSS).
   2. Move 2: CUSS → CUPS. 12 accepted words are one letter away; 3 of those keep a shortest route (CUBS, CUPS, CUTS).
   3. Move 3: CUPS → COPS. 10 accepted words are one letter away; 1 of those keeps a shortest route (COPS).
   4. Move 4: COPS → COOS. 20 accepted words are one letter away; 1 of those keeps a shortest route (COOS).
   5. Move 5: COOS → COOP. 15 accepted words are one letter away; 1 of those keeps a shortest route (COOP).
   6. Move 6: COOP → POOP. 14 accepted words are one letter away; 1 of those keeps a shortest route (POOP).

3. Route 3: fuss → cuss → cuts → cots → coos → coop → poop

   1. Move 1: FUSS → CUSS. 9 accepted words are one letter away; 3 of those keep a shortest route (CUSS, MUSS, SUSS).
   2. Move 2: CUSS → CUTS. 12 accepted words are one letter away; 3 of those keep a shortest route (CUBS, CUPS, CUTS).
   3. Move 3: CUTS → COTS. 18 accepted words are one letter away; 1 of those keeps a shortest route (COTS).
   4. Move 4: COTS → COOS. 18 accepted words are one letter away; 1 of those keeps a shortest route (COOS).
   5. Move 5: COOS → COOP. 15 accepted words are one letter away; 1 of those keeps a shortest route (COOP).
   6. Move 6: COOP → POOP. 14 accepted words are one letter away; 1 of those keeps a shortest route (POOP).

4. Route 4: fuss → muss → moss → boss → boos → boop → poop

   1. Move 1: FUSS → MUSS. 9 accepted words are one letter away; 3 of those keep a shortest route (CUSS, MUSS, SUSS).
   2. Move 2: MUSS → MOSS. 16 accepted words are one letter away; 1 of those keeps a shortest route (MOSS).
   3. Move 3: MOSS → BOSS. 19 accepted words are one letter away; 2 of those keep a shortest route (BOSS, MOOS).
   4. Move 4: BOSS → BOOS. 16 accepted words are one letter away; 1 of those keeps a shortest route (BOOS).
   5. Move 5: BOOS → BOOP. 21 accepted words are one letter away; 1 of those keeps a shortest route (BOOP).
   6. Move 6: BOOP → POOP. 12 accepted words are one letter away; 1 of those keeps a shortest route (POOP).

5. Route 5: fuss → muss → moss → moos → boos → boop → poop

   1. Move 1: FUSS → MUSS. 9 accepted words are one letter away; 3 of those keep a shortest route (CUSS, MUSS, SUSS).
   2. Move 2: MUSS → MOSS. 16 accepted words are one letter away; 1 of those keeps a shortest route (MOSS).
   3. Move 3: MOSS → MOOS. 19 accepted words are one letter away; 2 of those keep a shortest route (BOSS, MOOS).
   4. Move 4: MOOS → BOOS. 16 accepted words are one letter away; 3 of those keep a shortest route (BOOS, COOS, MOOR).
   5. Move 5: BOOS → BOOP. 21 accepted words are one letter away; 1 of those keeps a shortest route (BOOP).
   6. Move 6: BOOP → POOP. 12 accepted words are one letter away; 1 of those keeps a shortest route (POOP).

6. Route 6: fuss → muss → moss → moos → coos → coop → poop

   1. Move 1: FUSS → MUSS. 9 accepted words are one letter away; 3 of those keep a shortest route (CUSS, MUSS, SUSS).
   2. Move 2: MUSS → MOSS. 16 accepted words are one letter away; 1 of those keeps a shortest route (MOSS).
   3. Move 3: MOSS → MOOS. 19 accepted words are one letter away; 2 of those keep a shortest route (BOSS, MOOS).
   4. Move 4: MOOS → COOS. 16 accepted words are one letter away; 3 of those keep a shortest route (BOOS, COOS, MOOR).
   5. Move 5: COOS → COOP. 15 accepted words are one letter away; 1 of those keeps a shortest route (COOP).
   6. Move 6: COOP → POOP. 14 accepted words are one letter away; 1 of those keeps a shortest route (POOP).

7. Route 7: fuss → muss → moss → moos → moor → poor → poop

   1. Move 1: FUSS → MUSS. 9 accepted words are one letter away; 3 of those keep a shortest route (CUSS, MUSS, SUSS).
   2. Move 2: MUSS → MOSS. 16 accepted words are one letter away; 1 of those keeps a shortest route (MOSS).
   3. Move 3: MOSS → MOOS. 19 accepted words are one letter away; 2 of those keep a shortest route (BOSS, MOOS).
   4. Move 4: MOOS → MOOR. 16 accepted words are one letter away; 3 of those keep a shortest route (BOOS, COOS, MOOR).
   5. Move 5: MOOR → POOR. 8 accepted words are one letter away; 1 of those keeps a shortest route (POOR).
   6. Move 6: POOR → POOP. 7 accepted words are one letter away; 1 of those keeps a shortest route (POOP).

8. Route 8: fuss → suss → sums → sump → pump → pomp → poop

   1. Move 1: FUSS → SUSS. 9 accepted words are one letter away; 3 of those keep a shortest route (CUSS, MUSS, SUSS).
   2. Move 2: SUSS → SUMS. 12 accepted words are one letter away; 1 of those keeps a shortest route (SUMS).
   3. Move 3: SUMS → SUMP. 14 accepted words are one letter away; 1 of those keeps a shortest route (SUMP).
   4. Move 4: SUMP → PUMP. 10 accepted words are one letter away; 1 of those keeps a shortest route (PUMP).
   5. Move 5: PUMP → POMP. 11 accepted words are one letter away; 1 of those keeps a shortest route (POMP).
   6. Move 6: POMP → POOP. 6 accepted words are one letter away; 1 of those keeps a shortest route (POOP).

Hardest step: Move 5 from BOOS to BOOP in the second half. Only 1 of 21 possible changes keeps a shortest route, the lowest proportion along any shortest ladder.

Every first move

FUSS has 9 accepted words one letter away. The groups below separate choices that keep the shortest distance from choices that add moves.

Position across all archive puzzles

Ladder length

Tied for #58 longest (144 puzzles tied).

Number of shortest routes

#310 by fewest shortest routes (18 puzzles tied).

Previous and next puzzle

• Previous #441 CART: 5 moves, 3 shortest routes.

Each ladder changes one letter per move. The word list checks which four-letter words are accepted; breadth-first search measures the minimum distance to POOP, and routes with the same minimum distance are counted separately. This analysis uses Poople's accepted word list (2,398 words).