# Prime number snake (2)

This question is inspired by prime number snake. In the following grid, you have to place a number snake of numbers 1 to 100. Consecutive numbers have to go into neighboring cells.

Numbers in grey cells have to be prime numbers. Number 1 has to be placed into the yellow cell.

I claim that the grid above is uniquely solvable.

• Congratulations daw! Very nice. This was what I was aiming for when I handmade the original puzzle, one with a unique solution. If the position of 1 is not specified, how many solutions does the puzzle have? Commented Jan 27, 2020 at 0:53
• It would still have only one solution.
– daw
Commented Jan 27, 2020 at 6:56
• A bit late now, but given that uniqueness wasn't affected, I can't help feeling it would have been a cleaner puzzle if (like the original) it left the position of '1' to be deduced by the solver - could have created a few more blind alleys, or an opportunity for someone to post a "partial" indicating how they'd proved it couldn't be in the other place... Commented Jan 27, 2020 at 8:16
• @Steve I agree. I will use with my students without the 1 and see how it goes. Commented Jan 27, 2020 at 15:42
• @daw I am trying to design a similar puzzle in which the snake is a loop (it ends were it begins), and with a unique solution, like yours. Perhaps you can find one sooner than me! Commented Jan 27, 2020 at 15:44

(The earlier version of this answer contained more praise for this puzzle, sometimes comparing it to the earlier one. I only now noticed that this snake was indeed not posted by the OP of the original one, so I have now toned it down a bit.)

Here's the solution I found:

Some things I particularly liked:

* The 7-step run at 89-97 isn't instantly visible, but once you place 2 and 3 with some minor logic required, it becomes apparent where it must be.
* The snake follows the edge a lot, so that part is easy to place. This keeps the difficulty level nicely in check.
* There's still enough confusion 16-67 region that the puzzle is by no means trivial.

All in all, this snake strikes the exact sweet spot where it's not overly difficult, but it's still rewarding to solve.

May I have another? :-)

• I don't know why the different poster makes the complimentary notes in your first draft answer any less applicable. Well done, @daw!
– Rubio
Commented Jan 28, 2020 at 11:17