r/mathpuzzles • u/numstep • 8d ago

Recreational maths Numstep: The self-avoiding walk puzzle

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Hey, I'm launching a new puzzle.

Create a numbered step, self-avoiding walk through every white square. No diagonals.

Follow my socials for daily puzzles.

3 Upvotes

80% Upvoted

12 comments sorted by

1

u/SonicLoverDS 8d ago

Oh, look, it's a Creeper with lazy eye.

1

u/numstep 8d ago

pareidolia, the logic puzzle... I'm game

1

u/carljohanr 7d ago

Unless I'm missing something the big puzzle has multiple solutions. (Checked in Codex and it has 20 solutions). Here is the only part that's forced:

## ## 15 14 ## 10 09 08 07
.. .. 16 13 12 11 ## ## 06
.. 20 .. .. .. 60 ## ## 05
.. .. .. .. .. .. ## ## 04
.. .. .. .. .. .. .. .. 03
32 31 30 .. .. .. .. .. 02
33 ## ## ## ## .. .. 50 01
34 ## 38 39 ## 43 44 49 48
35 36 37 40 41 42 45 46 47

1

u/numstep 7d ago

Quite probably. In a local group (say 3x3 attempting to link n and n+8) there are two ways to get from opposite corners, which gives trivially different solutions. Or drawing two pairs of adjacent walks can have multiple configurations.

I am trying to strike a balance between visually appealing, challenging to a casual puzzler and mathematically rich... Having a single distinct solution is a casualty.

I considered adding in "walls" between two white squares to restrict the multiple solutions down to a single one... But my conclusion is that this makes the problem too easy to solve, more like a labyrinth and leas like a maze.

Do you think the puzzle is spoilt by having multiple possible answers?

try today's grids

2

u/carljohanr 7d ago

Yes

1

u/numstep 7d ago

Thank you for the feedback.

Do you think the puzzle befonea too easy? Or is just less satisfying?

Would you prefer a larger grid? Fewer revealed squares? Or are you not a fan of the format all together?

2

u/chrisvenus 6d ago

The reason I find multiple solutions unsatisfying because I solve logic puzzles logically. I look for the forced moves that logically must exist and keep going til I have the solution. If there are multiple solutions then there is no logical forced path to the solution which means you are basically just trying it to see if it works and hoping for the best. This is not what I want in a puzzle.

1

u/numstep 6d ago

Cool. I shall take this on board for my next round of redrafts

1

u/numstep 6d ago

Cool. I shall take this on board for my next round of redrafts