Professor Layton alternate solutions

[HelpTheWretched]

Here's something kind of weird in Professor Layton and the Last Specter (aka Spectre's Call) that I found by complete accident. (The weird thing is at the bottom, after the story.)

When I solved puzzle #161, "Lily Pad Leapfrogs 2", the solution shown on the recap screen was different than the way I solved it. I found this notable because the puzzles in the Professor Layton series are very expertly made, and there are rarely any alternate solutions unless they're mentioned in the recap text, except when it's obvious since the puzzles can be mirrored, or they're solitaire types that are commonly known to have multiple solutions.

Here's the puzzle:



*SPOILERS BELOW* And this is the solution it shows:


I forgot to write down my solution, so a while later I did the only sensible thing: write a program to brute-force the puzzle and list any/every alternate solution. The results were a little more than I'd expected!

(D=Down, U=Up, L=Left, R=Right)

1: DRRRUDLLLLUUURLRRRDLLDURDURULRULDRR
2: DRRRUDLLLLUUURLDRDURUUUURRDLLDRRUDR
3: DRRRUDLLLLUUURLDUDRRULURRDLDDURUURR
4: DRRRUDLLLLUUURLDUDRDURURUDLUURRDLDR
5: DRRRUDLLLLUUURLDUDRDURUURDULURRDLDR
6: DRRRUDLLUDLDLLUUURLDUDRRUDLUURRDLDR
7: DRRRUDLLUDLURUURDLLDURDLLUUURLRDDRR
8: DRRRUDLLUDLUDLLUUURLRDDRDUURDLLDURR
9: DRRDRUULRLDURDLLUUURLRDDRUURDLLDURR
10: DRRDRUULRUDLUURRDLLDRDURDLLUUURLDRR
11: DRRDRUULDDLLUUURLRRRDLLDURDUURULDRR
12: DRRDRUULDLDRLLUUURLDUDRRUDLUURRDLDR
13: DRRDRUULDLURUURDLLDURDRLLUUURLRDDRR
14: DRRDRUULDLUDRLLUUURLRDDRDUURDLLDURR
15: DRRDRUULLRUURDLLDURDURDLLUUURLRDDRR
16: DRRDRUULLDURDLLUUURLRDDRDUURDLLDURR
17: DRRDRUULURDLDURDLLUUURLRDRURDLLDURR
18: DRRDRUULURDULURRDLLDRDURDLLUUURLDRR
19: DRRDRUULUURDDLDURDLLUUURLRRRDLLDURR
20: DRRDRUULUUURRDLDDURDLLUUURLDUDRRUDR
21: DRRDLRUULDLDLLUUURLDUDRRUDLUURRDLDR
22: DRRDLRUULDLURUURDLLDURDLLUUURLRDDRR
23: DRRDLRUULDLUDLLUUURLRDDRDUURDLLDURR
24: DRRLDLLUUURLRRRDLLDURDUURDRUULUURDR
25: DRRLDLLUUURLRDRURDLLDURDUURDRUULURR
26: DRRLLDRLLUUURLDUDRRDRUULURULURRDLDR
27: DRRLLDLLUUURLRRRDDUDLLULRUDLULLDURR
28: DRRLLDLLUUURLRRRDDUDLLUUURDDLULDURR
29: DRRLLDLLUUURLRDRURDDUDLLUURDLULDURR
30: DRRLLDLLUUURLRDDRDUURDDUDLLULULDURR
31: DRRLLDLLUUURLRDDRUURDDUDLLURLULDURR
32: DRRLLDLLUUURLDDRULRURRDDUDLLURUDLLR
33: DRRLLDLLUUURLDUDRRDLRUULURULURRDLDR
34: DRRLLDLLUUURLDUDRURURRDDUDLLURUDLLR
35: DRRLLURULLLDURDLLUUURLRRRDDUDLLUURR
36: DRRLLUDLLUUURLRRRDDUDLLURUDLULLDURR
37: DRRLLUDLLUUURLRRRDDUDLLUURDULLLDURR
38: DRRLLUULDURDLLUUURLRRRDDUDLLURULDRR
39: DRRUDRUULDLUDRLLUUURLRDDRUURDLLDURR
40: DRRUDRUULLDURDLLUUURLRDDRUURDLLDURR
41: DRRUDRUULURULURRDLLDRDURDLLUUURLDRR
42: DRRUDLRUULDLUDLLUUURLRDDRUURDLLDURR
43: DRRULDURUURUURDDUDLLLLUUURLRDLLDURR
44: DRRUUDLUURRDDUDLLUDLDLLUUURLDUDRUDR
45: DRRUULURRDDUDLLLLUUURLDUDRUDDURUURR
46: DRRUUURDDUDLLUDLUULDURDLLUUURLRDDRR
47: DRURURRDDUDLUUUDLDDLDRLLUUURLDDRUDR
48: DRUDRURURRDDUDLUUUDLDDLDRLLUUURLDRR
49: DRUDURDRLLUUURLRRRDDUDLULLUURDDRUDR
50: DRUDURDURRRUDLLLLUUURLRRRDLRDDLRUDR
51: DRUDURDUUURDDDDLLUUURLRRRDDUDLUUUDR
52: DRUDULUURLRRRDDUDLULLDLLRURLURRDLLR
53: DRUDULUURLRRRDDUDLULLDLLRULRUDLULDR
54: DRUDULUURLRRRDDUDLULLDLLRUUURDDLUDR
55: DRUDULUURLRRRDDUDLULLURULLDDLLRUURR
56: DRUDULUURLRRRDDUDLULLUDLLRURUDLULDR
57: DRUDULUURLRRRDDUDLULLUDLLRUURDULLDR
58: DRUDULUURLRRRDDUDLULLUURDLDLLRURUDR
59: DRUDULUURLRRRDDUDLULLUUDDLLRURULDRR
60: DRUDULUURLRRRDDULDLDLLRRLUULURRDLLR
61: DRUDULUURLRRRDDULDLUDLLRRLUUUDLULDR
62: DRUDULUURLRRRDDULDLUURDLDLLRRLUUUDR
63: DRUDULUURLRRRDDULDLUUDDLLRRLUUULDRR
64: DRUDULUURLRRRDDULUULDDLLRRLULLURUDR
65: DRUDULUURLRRRDLRRDDDULLUDLLRRUULULR
66: DRUDULUURLRRRDLRDLDLLRRLURULDLURUDR
67: DRUDULUURLRRRDLDDLLRRLURULDLURULDRR
68: DRUDULUURLRDRURDDUDLULLDLLRUURDLUDR
69: DRUDULUURLRDDRDUURDDUDLULLDLLRULUDR
70: DRUDULUURLRDDRUURDDUDLULLDLLRURLUDR
71: DRUDULUURLRDDRUURDDULDLDLLRRLUULUDR
72: DRUDULUURLRDLDDLLRRLULLURUURDDULURR
73: DDRRLURULDLURUURDLDDLUUDULUURLRDDRR
74: DDRRLURULDLUDLUUDULUURLRDDRDUURDLDR
75: DDRRLULLDLUUDULUURLRRRDDULRLURRDLLR
76: DDRRLULLDLUUDULUURLRRRDDULLRUDLULDR
77: DDRRLULLDLUUDULUURLRRRDDULUURDDLUDR
78: DDRRLULLDLUUDULUURLRDRURDDULURDLUDR
79: DDRRLULLDLUUDULUURLRDDRDUURDDULLUDR
80: DDRRLULLDLUUDULUURLRDDRUURDDULRLUDR
81: DDRRLULLURULLDDLUUDULUURLRRRDDULURR
82: DDRRLULLUDLUUDULUURLRRRDDULRUDLULDR
83: DDRRLULLUDLUUDULUURLRRRDDULURDULLDR
84: DDRRLULLUURDLDLUUDULUURLRRRDDULRUDR
85: DDRRLULLUUDDLUUDULUURLRRRDDULRULDRR
86: DDRRLUUUURDDULDLUUDDLUUDULUURLRDDRR
87: DDRRUULRDULLUDLUUDULUURLRRRDLRRDLLR
88: DDRRUULLRDULLDLUUDULUURLRRRDLRRDLLR
89: DDRRUULLRDULLDLUUDULUURLRDDRUURDLDR
90: DDRRUULURDDULLUDLUUDULUURLRDRURDLDR
91: DDRRUULUURDDDULLUDLUUDULUURLRRRDLDR
92: DDRLRULUDULUURLRRRDDUDLULURLURRDLLR
93: DDRLRULUDULUURLRRRDDUDLULULRUDLULDR
94: DDRLRULUDULUURLRRRDDUDLULUUURDDLUDR
95: DDRLRULUDULUURLRDRURDDUDLULUURDLUDR
96: DDRLRULUDULUURLRDDRDUURDDUDLULULUDR
97: DDRLRULUDULUURLRDDRUURDDUDLULURLUDR
98: DDRLUUDULUURLRRRDDUDLULUUULDDUURUDR
99: DDRLUUDULUURLRRRDDUDLUULDURUURULLDR
100: DDRLUUDULUURLRRRDDUDLUULUDDURUUURDR
101: DDRLUUDULUURLRRRDLRRDDLDURRDRUULULR
102: DDRLUUDULUURLRRRDLRDLDURRDRUULLRUDR
103: DDRLUUDULUURLRRRDLDDURRDRUULLRULDRR
104: DDRLUUDULUURLRDRURDDUDLUULUDDURUURR
105: DDRLUUDULUURLRDLDDUURUURDDUDLULUURR
106: DDRURUURDDUDLULLUUDDLUUDULUURLRDDRR
107: DDRUDLDLUUDULUURLRRRDDUDLUULURRDLLR
108: DDRUDLDLUUDULUURLRDDRUURDDUDLUULUDR
109: DDRUDLUDLUUDULUURLRRRDDUDLUUUDLULDR
110: DDRUDLUURDLDLUUDULUURLRRRDDUDLUUUDR
111: DDRUDLUUDDLUUDULUURLRRRDDUDLUUULDRR
112: DDRUURDUURDDUDLULLUDLUUDULUURLRDLDR
113: DDRUUULDDLUUDULUURLRRRDDUDLULLURUDR
114: DDUUURLRRRDDUDLLLRULRLULRUDLULLDURR
115: DDUUURLRRRDDUDLLLRULRLUUURDDLULDURR
116: DDUUURLRRRDDUDLLLURLUUULLDURDUURUDR
117: DDUUURLRRRDDUDLLLURULDURUURULLLDURR
118: DDUUURLRRRDDUDLLLURULULDURDURUUURDR
119: DDUUURLRRRDDUDLLLUUDURDUUURDDDRUUDR
120: DDUUURLRRRDDUDLLUDLUDLURUUDLULLDURR
121: DDUUURLRRRDDUDLLUDLUULDURDLURUULDRR
122: DDUUURLRRRDDUDLLUUULLDURDLURLLURUDR
123: DDUUURLRRRDDUDLULDLUUDURDUUURDDRUDR
124: DDUUURLRRRDDUDLUULURRDLDDDLRULUDURR
125: DDUUURLRRRDDUDLUULURRDLDDLDRLUUDURR
126: DDUUURLRRRDLRRDLDRLDURRRUDLLLUUDURR
127: DDUUURLRRRDLRDDDRRUDLLLUUDURDUURUDR
128: DDUUURLRRRDLLDURDRLURDRUULDLURULDRR
129: DDUUURLRRRDLLDURDRLURLLURDRUULUURDR
130: DDUUURLRRRDLLDURDLURRUDLLUDLURULDRR
131: DDUUURLRRRDLLDURDLURDLRUULDLURULDRR
132: DDUUURLRRRDLLDURDLURLLURDLRUULUURDR
133: DDUUURLRRRDLLDURDURDLURDRUULLRULDRR
134: DDUUURLRDRURDDUDLLLRULRLUURDLULDURR
135: DDUUURLRDRURDDUDLLLURULULDURDURUURR
136: DDUUURLRDRURDLLDURDRLURLLURDRUULURR
137: DDUUURLRDRURDLLDURDLURLLURDLRUULURR
138: DDUUURLRDDRDUURDDUDLLLRULRLULULDURR
139: DDUUURLRDDRUURDDUDLLLRULRLURLULDURR
140: DDUUURLRDDRUURDDUDLLUDLDLURULULDURR
141: DDUUURLRDLLDURDLURLLURUURDDUDLLUURR
142: DDUUURLRDLLDURDUURUURDDUDLLLURLUURR
143: DDUUURLDRDURDLURDRUULUUURRDLLDRRUDR
144: DDUUURLDDRRUDLDDRRUDLLLRULURURRDLDR
145: DDUUURLDDRULRURRDDUDLLLRULRLURUDLLR
146: DDUUURLDDRULRURRDDUDLLUDLDLURUUDLLR
147: DDUUURLDDDURURRDDUDLLLRURRUUDLDLUDR
148: DDUUURLDDDURURRDDUDLUUUDLDDDLRUUUDR
149: DDUUURLDUDRRULURRDLDDURDLURDRUULURR
150: DDUUURLDUDRDURDLURDRUULRUDLUURRDLDR
151: DDUUURLDUDRDURDLURDRUULURDULURRDLDR
152: DDUUURLDUDRDURDLURUDRUULURULURRDLDR
153: DDUUURLDUDRURURRDDUDLLLRULRLURUDLLR
154: DDUUURLDUDRURURRDDUDLLUDLDLURUUDLLR
155: DDUUURLDUDRUDDURUUUURRDDUDLLLURUUDR
156: DDUUURLDUDDRRUDLLLRURULRUDLUURRDLDR
157: DDUUURLDUDDRDRUULDDLRUURUDLUURRDLDR
158: DDUUURLDUDDRLDLRUURDRUULURULURRDLDR
159: DDUUURLDUDDRLURUDLUURRDDUDLLLRUUUDR
160: DDUUURLDUDDRLUURDULURRDDUDLLLRUUUDR
161: DDUUURLDUDDRUUDLUURRDDUDLLLRURULUDR

(Note: These solutions don't include the initial "R" to get on the 1st lily pad, nor the final "R" to reach the goal.)

Go ahead, try any of them! As it turns out, puzzle #161 has 161 alternate solutions. I wonder if they planned that?

I found another neat tidbit by accident, because I suck in certain programming environments. My "check if all lily pads were touched" code wasn't working, so I changed it to simply print any 35-jump combinations it could find, along with the coordinate of the last lily pad it lands on. They all ended on the same pad next to the goal. In other words, it's impossible to touch all the lily pads without properly completing the puzzle.

Having so many solutions also made it harder to solve, not easier, since trial-and-error couldn't eliminate nearly as many "error" paths.