# Wednesday's Fujisan Problem

Four Shinto Priests have traveled from their various prefectures in pilgrimage to the top of Mount Fuji. You must find pathways for them to move up and down the mountain until they can all achieve the peak. Often, this will require you to guide them into positions from which they can assist each other. See Monday's problem for the full rules.

Today's problem is a little more challenging. Good luck, and post your solution as an answer with each move labeled for pawn A, B, C, or D, the direction, and the number of steps. Don't worry if you don't have dominoes, you can print out the diagram. If someone else has posted an answer, see if you can find one with fewer moves.

• Why do we always start with C, haha. Commented Aug 10, 2022 at 14:51
• This puzzle and others like it would be improved by adding the [no-computers] tag, as modern hardware is more than sufficient to find the solution through brute force. Commented Aug 10, 2022 at 17:18
• I love that you wrote a solver, @TimC. My only suggestion is to wait 48 hours after I post Friday's problem to let the hand solvers find the best solution they can before you run your solver. Commented Aug 11, 2022 at 0:38

This is a computerized solution found by the brute force solver I wrote last time. I encourage solvers to treat it as a sort of "answer key" (because computerized solutions are boring) and have broken it into multiple spoilers to better facilitate partial reveals.

Broken down by segments corresponding to justhalf's solution above, the number of moves in each section are:

Step 1:

Priest C makes 9 moves to unblock Priest A

Step 2:

Priests C and A make 10 moves to unblock priest D

Step 3 and 4:

Priests C, A, and D make 17 moves to unblock priest B

Step 5:

The four priests together make 8 moves to reach the summit.

For a total of

44 moves

The moves are

Step 1:

1: C<4 : Move Priest C to the top of domino 9
2: C : Move Priest C to the bottom of domino 9
3: C>1 : Move Priest C to the bottom of domino 10
4: C : Move Priest C to the top of domino 10
5: C>2 : Move Priest C to the top of domino 12
6: C<4 : Move Priest C to the top of domino 8
7: C : Move Priest C to the bottom of domino 8
8: C<5 : Move Priest C to the bottom of domino 3
9: C : Move Priest C to the top of domino 3

Step 2:

10: A>3 : Move Priest A to the top of domino 4
11: A : Move Priest A to the bottom of domino 4
12: A>1 : Move Priest A to the bottom of domino 5
13: C : Move Priest C to the bottom of domino 3
14: C>5 : Move Priest C to the bottom of domino 9
15: A>5 : Move Priest A to the bottom of domino 11
16: C>1 : Move Priest C to the bottom of domino 10
17: C : Move Priest C to the top of domino 10
18: C>2 : Move Priest C to the top of domino 12
19: C : Move Priest C to the bottom of domino 12

Steps 3 and 4:

20: D<1 : Move Priest D to the bottom of domino 10
21: C : Move Priest C to the top of domino 12
22: C<4 : Move Priest C to the top of domino 8
23: C : Move Priest C to the bottom of domino 8
24: C<5 : Move Priest C to the bottom of domino 3
25: C>1 : Move Priest C to the bottom of domino 4
26: C>1 : Move Priest C to the bottom of domino 5
27: D : Move Priest D to the top of domino 10
28: A<1 : Move Priest A to the bottom of domino 10
29: D>2 : Move Priest D to the top of domino 12
30: D<4 : Move Priest D to the top of domino 8
31: D : Move Priest D to the bottom of domino 8
32: A<5 : Move Priest A to the bottom of domino 3
33: D<4 : Move Priest D to the bottom of domino 2
34: A : Move Priest A to the top of domino 3
35: C<3 : Move Priest C to the bottom of domino 1
36: A : Move Priest A to the bottom of domino 3

Step 5:

37: B>1 : Move Priest B to the bottom of domino 4
38: A>3 : Move Priest A to the bottom of domino 7
39: A<0 : Move Priest A to the bottom of domino 6
40: C>3 : Move Priest C to the bottom of domino 7
41: B : Move Priest B to the top of domino 4
42: D : Move Priest D to the top of domino 2
43: D>3 : Move Priest D to the top of domino 6
44: B>2 : Move Priest B to the top of domino 7

• Nice. So I can still shave 2/5/1 moves from step 2/3+4/5. Hmm Commented Aug 10, 2022 at 17:41
• @justhalf - Interestingly, it seems like there are multiple meaningfully distinct solutions of minimal length. While freeing priest D requires two priests on two specific tiles, your new Part 2 solution ends up with priests A and C transposed from the one I've posted, but paths are the same length. Commented Aug 10, 2022 at 17:58
• Oo, interesting. I did try a few alternatives, but only found my new Part 2 with length 10. Optimizing step 3&4 is quite challenging manually though, so many possibilities. But good to know I've got the optimal ones for the other steps. Commented Aug 11, 2022 at 10:43
• Looks like move 43 is invalid, because that piece is already at the target position. Move 44 is also invalid, because the target position is already occupied. 🐛? Commented Aug 13, 2022 at 1:34
• Oops! Looks like my solver had a bug that would allow priests to move into y coordinates that didn't exist as long as they were already on the peak. I've fixed the bug and updated the solution. Number of steps did not change. Commented Aug 13, 2022 at 8:25

Notes:

A needs 1 help to do A>3, B needs 3 help to do B>1, C can do C<4 immediately, D needs 2 help to do D<1. So we need to move C to help A, then both to help D, then all of them to help B, and finally enter the peak.

The moves:

Step 1:

C<4 C C>1 C C>2 C<4 C C<5 C (9 moves, unlocks A)

Step 2:

A>3 A C>2 A A>4 C>4 A>2 C>1 A C (10 moves, unlocks D)

Step 3:

D<1 D D>2 D<4 D D<5 D>1 D>1 D A A<4 A<3 A D C<1 C<5 (16 moves, ACD to left side)

Step 4:

D D<3 C A<3 D C (6 moves, unlocks B)

Step 5:

B>1 A>3 A<1 D B D>3 B>2 C>3 (8 moves, all to peak)

Total: 49 moves.