# Friday'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, and Wednesday's problem for more practice.

Today's problem is even 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. If someone else has posted an answer, see if you can find one with fewer moves.

# Computer Generated Solution

All four priests to the mountain in

65 moves.

Step 1:

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

Step 2:

8: D<2 : Move Priest D to the bottom of domino 10
9: B<3 : Move Priest B to the bottom of domino 8
10: B<3 : Move Priest B to the bottom of domino 5
11: B : Move Priest B to the top of domino 5
12: B<4 : Move Priest B to the top of domino 1
13: B : Move Priest B to the bottom of domino 1
14: B>1 : Move Priest B to the bottom of domino 2
15: B>2 : Move Priest B to the bottom of domino 4
16: B : Move Priest B to the top of domino 4
17: B>5 : Move Priest B to the top of domino 9
18: D : Move Priest D to the top of domino 10
19: D<1 : Move Priest D to the top of domino 8
20: B : Move Priest B to the bottom of domino 9
21: D : Move Priest D to the bottom of domino 8
22: B<3 : Move Priest B to the bottom of domino 5
23: B>5 : Move Priest B to the bottom of domino 11
24: B : Move Priest B to the top of domino 11
25: D : Move Priest D to the top of domino 8
26: D>3 : Move Priest D to the top of domino 12

Step 3:

27: C<1 : Move Priest C to the top of domino 10
28: B : Move Priest B to the bottom of domino 11
29: B<3 : Move Priest B to the bottom of domino 8
30: B<3 : Move Priest B to the bottom of domino 5
31: B : Move Priest B to the top of domino 5
32: B<4 : Move Priest B to the top of domino 1
33: B : Move Priest B to the bottom of domino 1
34: B>1 : Move Priest B to the bottom of domino 2
35: B>2 : Move Priest B to the bottom of domino 4
36: B : Move Priest B to the top of domino 4
37: B>5 : Move Priest B to the top of domino 9
38: B : Move Priest B to the bottom of domino 9
39: D : Move Priest D to the bottom of domino 12
40: D<3 : Move Priest D to the bottom of domino 8
41: C : Move Priest C to the bottom of domino 10
42: C<3 : Move Priest C to the bottom of domino 5
43: C : Move Priest C to the top of domino 5
44: B<3 : Move Priest B to the bottom of domino 5
45: C<4 : Move Priest C to the top of domino 1
46: C : Move Priest C to the bottom of domino 1
47: C>1 : Move Priest C to the bottom of domino 2
48: C>2 : Move Priest C to the bottom of domino 4
49: D<3 : Move Priest D to the bottom of domino 3
50: B : Move Priest B to the top of domino 5
51: B<4 : Move Priest B to the top of domino 1
52: C : Move Priest C to the top of domino 4
53: D : Move Priest D to the top of domino 3

Step 4:

54: A>2 : Move Priest A to the top of domino 5
55: A : Move Priest A to the bottom of domino 5
56: B : Move Priest B to the bottom of domino 1
57: B>4 : Move Priest B to the bottom of domino 6
58: B : Move Priest B to the top of domino 6
59: D : Move Priest D to the bottom of domino 3
60: D<2 : Move Priest D to the bottom of domino 1
61: D>4 : Move Priest D to the bottom of domino 6
62: C : Move Priest C to the bottom of domino 4
63: C>1 : Move Priest C to the bottom of domino 7
64: C : Move Priest C to the top of domino 7
65: A>1 : Move Priest A to the bottom of domino 7

• Thanks for solving all three puzzles this week! 🎉 Aug 15, 2022 at 14:52

Notes:

A needs 3 help to do A>2
B needs 0 help to do B>3
C needs 2 help to do C<1
D needs 1 help to do D<2
So the order is B, D, C, A.

Step 1:

B>3 B<1 B>2 B B>5 B>3 B (7 moves, unlocks D)

Step 2:

D<2 B<3 B<3 B B<4 B B>1 B>2 B B>5 D D<1 D B B<3 B>5 B D D>3 (19 moves, unlocks C)

Step 3:

C<1 C D D<3 D<3 D D<4 D D>1 D>2 D D>5 C B<1 B D C C<3 C C<4 C C>1 C>2 D<3 B<3 D<1 D B C (29 moves, unlocks A)

Step 4:

A>2 D D>4 A C B B>1 B B<1 C>1 C A>1 (12 moves, all to peak)

Total: 67 moves

Moving the first priest from the right side to the left side requires intricate maneuver, exemplified in Step 2 and Step 3.

• I'm holding off on posting the computer-generated solution until Sunday, but I'll confirm that Steps 1 and 2 of this solution are optimal. Aug 13, 2022 at 8:35
• Thanks! I'm surprised Step 4 is not optimal. Probably the starting point is different, I suppose? There are 4 possible starting points for Step 4. Aug 13, 2022 at 8:51
• Indeed. In fact, the solution I have takes one move longer to do step 4, but makes up for it with a shorter step 3, for a (very slightly) shorter overall solution. Aug 13, 2022 at 9:34
• I see. Yea, I didn't consider different Step 3 that led to longer Step 4, haha Aug 13, 2022 at 10:40
• Thanks for solving all three puzzles this week! 🎉 Aug 15, 2022 at 14:53