Poople #441: CART to POOP

Path analysis

This route reaches POOP in 5 moves. Breadth-first search reaches every route with fewer moves first, so POOP cannot be reached in fewer than 5 moves from CART.

Moves

5

Difficulty

Hard

Shortest paths

3

The dictionary has 3 equally short routes; the route below is one of them.

1. Move 1: CART → CAST — change the 3rd letter from R to S.
2. Move 2: CAST → COST — change the 2nd letter from A to O.
3. Move 3: COST → COOT — change the 3rd letter from S to O.
4. Move 4: COOT → COOP — change the 4th letter from T to P.
5. Move 5: COOP → POOP — change the 1st letter from C to P.

Computed route analysis

3 equally short ladders connect CART to POOP in 5 moves, making this a hard puzzle. The narrowest decision comes in the second half, at COOT: only 1 of 17 possible one-letter changes from COOT can keep a shortest route on track. The counts use Poople's accepted word list (2,398 words).

Shortest word ladders

This puzzle has 3 shortest routes. The archive contains 441 puzzles. Showing 3 shortest routes.

1. Route 1: cart → carp → camp → comp → coop → poop

   1. Move 1: CART → CARP. 16 accepted words are one letter away; 2 of those keep a shortest route (CARP, CAST).
   2. Move 2: CARP → CAMP. 10 accepted words are one letter away; 1 of those keeps a shortest route (CAMP).
   3. Move 3: CAMP → COMP. 11 accepted words are one letter away; 1 of those keeps a shortest route (COMP).
   4. Move 4: COMP → COOP. 8 accepted words are one letter away; 2 of those keep a shortest route (COOP, POMP).
   5. Move 5: COOP → POOP. 14 accepted words are one letter away; 1 of those keeps a shortest route (POOP).

2. Route 2: cart → carp → camp → comp → pomp → poop

   1. Move 1: CART → CARP. 16 accepted words are one letter away; 2 of those keep a shortest route (CARP, CAST).
   2. Move 2: CARP → CAMP. 10 accepted words are one letter away; 1 of those keeps a shortest route (CAMP).
   3. Move 3: CAMP → COMP. 11 accepted words are one letter away; 1 of those keeps a shortest route (COMP).
   4. Move 4: COMP → POMP. 8 accepted words are one letter away; 2 of those keep a shortest route (COOP, POMP).
   5. Move 5: POMP → POOP. 6 accepted words are one letter away; 1 of those keeps a shortest route (POOP).

3. Route 3: cart → cast → cost → coot → coop → poop

   1. Move 1: CART → CAST. 16 accepted words are one letter away; 2 of those keep a shortest route (CARP, CAST).
   2. Move 2: CAST → COST. 14 accepted words are one letter away; 1 of those keeps a shortest route (COST).
   3. Move 3: COST → COOT. 11 accepted words are one letter away; 1 of those keeps a shortest route (COOT).
   4. Move 4: COOT → COOP. 17 accepted words are one letter away; 1 of those keeps a shortest route (COOP).
   5. Move 5: COOP → POOP. 14 accepted words are one letter away; 1 of those keeps a shortest route (POOP).

Hardest step: Move 4 from COOT to COOP in the second half. Only 1 of 17 possible changes keeps a shortest route, the lowest proportion along any shortest ladder.

Every first move

CART has 16 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 #201 longest (241 puzzles tied).

Number of shortest routes

#174 by fewest shortest routes (44 puzzles tied).

Previous and next puzzle

• Previous #440 CRUX: 7 moves, 4 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).