Poople #397: RISK 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 RISK.

Moves

6

Difficulty

Hard

Shortest paths

1

The dictionary has one shortest route for this puzzle.

1. Move 1: RISK → RISE — change the 4th letter from K to E.
2. Move 2: RISE → ROSE — change the 2nd letter from I to O.
3. Move 3: ROSE → POSE — change the 1st letter from R to P.
4. Move 4: POSE → POME — change the 3rd letter from S to M.
5. Move 5: POME → POMP — change the 4th letter from E to P.
6. Move 6: POMP → POOP — change the 3rd letter from M to O.

Computed route analysis

The hard puzzle from RISK has one shortest ladder to POOP, taking 6 moves. Its narrowest decision is in the first half, at ROSE: only 1 of 15 possible one-letter changes from ROSE can keep a shortest route on track. Counts use Poople's accepted word list (2,398 words).

Shortest word ladders

This puzzle has 1 shortest route. The archive contains 442 puzzles. Showing 1 shortest route.

1. Route 1: risk → rise → rose → pose → pome → pomp → poop

   1. Move 1: RISK → RISE. 4 accepted words are one letter away; 1 of those keeps a shortest route (RISE).
   2. Move 2: RISE → ROSE. 13 accepted words are one letter away; 1 of those keeps a shortest route (ROSE).
   3. Move 3: ROSE → POSE. 15 accepted words are one letter away; 1 of those keeps a shortest route (POSE).
   4. Move 4: POSE → POME. 13 accepted words are one letter away; 1 of those keeps a shortest route (POME).
   5. Move 5: POME → 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 3 from ROSE to POSE in the first half. Only 1 of 15 possible changes keeps a shortest route, the lowest proportion along any shortest ladder.

Every first move

RISK has 4 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

#1 by fewest shortest routes (99 puzzles tied).

Previous and next puzzle

• Previous #396 CARS: 5 moves, 10 shortest routes.
• Next #398 WHAT: 5 moves, 5 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).