• #### new puzzle: Extensions

From Steven Meyers@21:1/5 to All on Thu Jan 9 13:35:00 2020
Hello everyone,

Below is a write-up for my new puzzle, called Extensions. Any and all feedback is welcome.

Regards,

Steve

EXTENSIONS
Extensions is a pen-and-paper puzzle that was invented by Steven Meyers in November 2019. Thanks to Cameron Browne for considerable playtesting. It manifests as two main variants, Extensions 1 and Extensions 2. But first I will describe the general
setting of Extensions, and explain the Extensions mechanism that gives the puzzle its name.
Extensions takes place on a grid of islands. Some of the islands have numbers, and some do not. Bridges exist between islands. Each number represents the number of bridges extending in consecutive line from the island. (The bridges may extend
consecutively from the island upwards, downwards, to the left, and to the right.) Here is an example. The ‘.’s represent a non-numbered island.
. . . .
|
. . . .
|
. . –- 4 -- .

. . . .

The island numbered with a 4 has four bridges extending consecutively from it. Two bridges extend upward, one bridge extends to the left, and one bridge extends to the right. There are no bridges extending downward.

It’s important to remember that the extensions must be consecutive in order to contribute to the number. (That is, if there are any breaks, then the bridges beyond the breaks do not count towards the number on the island.) For instance, consider the
following example:

. . . .

. . . .

2 -- . . -- .
|
. . . .

Why isn’t the island numbered with a 3 rather than a 2? Because the bridge on the far right occurs after a break (that is, it is not consecutive) and therefore does not count toward the number.
A well-designed Extensions puzzle will have a solution that is both unique and deducible (no guessing required), and therefore is appropriate for pen-and-paper. A couple of practical techniques on solving: 1) When all the bridges extending
consecutively from a numbered island have been drawn in, go ahead and put a check mark next to the island so that you know the number has been “fulfilled,” so to speak. 2) When you can conclude that there is not a bridge between two islands, write
in “E” for empty. It’s just as important to deduce where there are no bridges as it is to deduce where there are bridges.
Here’s something to remember when solving: Sometimes a number will contain more information than would at first appear. Consider the following example:
. . . 2
. . . .
. . . .
. . . 3
At first it may seem that nothing definitive can be deduced about the island numbered with a 3, since you might jump to the conclusion that the 3 can be fulfilled entirely horizontally, entirely vertically, or any combination thereof. But upon closer
inspection this is not the case. The 3 cannot fulfill itself entirely vertically, because that would mean all the other numbers in the vertical line would have to be at least 3, and they are not. (There is a 2 at the top, and it cannot be consecutively
connected to the 3.) And so it can be concluded that there must be at least one bridge extending to the left from the 3.
The Extensions principle best manifests as two main variants, Extensions 1 and Extensions 2.
EXTENSIONS 1
1) There is a grid of islands.
2) Each number represents the number of bridges extending in consecutive line from the island.
3) The solution forms a single loop passing through all numbered islands. The loop can have no branches or crossings.
4) Non-numbered islands may, but do not have to be, part of the loop. (Note: A variant was tried where all islands have to be part of the loop, whether they are numbered or not. However this variant appears to be inferior.)
Here is a 4x4 puzzle for Extensions 1. The solution is unique and is deducible without guessing.
. 3 2 .

3 . . 3

2 2 . .

. . 2 4

Here’s the solution to the above puzzle:

. 3 –- 2 -- .
| |
3 -- . . 3
| |
2 2 -- . .
| | | |
. -- . 2 –- 4

Here’s another 4x4 puzzle for Extensions 1. The solution is unique and is deducible without guessing.

. . 3 .

3 . . 2

. . . .

. 3 . 4

You may wish to solve the puzzle above yourself.

Here’s a 6x6 puzzle for Extensions 1. The solution is unique and is deducible without guessing.

. . 5 . 3 .

5 2 2 . . 3

. 2 . 2 2 .

4 . . 3 2 .

. 2 . 2 . 2

5 . . 4 2 .

You may wish to solve the puzzle above yourself.

EXTENSIONS 2
1) There is a grid of islands.
2) Each number represents the number of bridges extending in consecutive line from the island.
3) The solution must form a single connected network of all islands, whether they are numbered or not.
(Note: A variant was tried where non-numbered islands did not necessarily have to be part of the single connected network. However this variant appears to be inferior.)
Here is a 4x4 puzzle for Extensions 2. The solution is unique and deducible without guessing.

1 . 2 1

4 5 . 4

4 . 3 .

1 4 . 3

Here’s the solution to the above puzzle:

1 . –- 2 1
| | |
4 –- 5 -- . –- 4
|
4 -- . –- 3 -- .
| | |
1 4 -- . –- 3

Here is another 4x4 puzzle for Extensions 2. The solution is unique and deducible without guessing.

1 . 1 4

2 . 1 .

4 . 4 3

2 2 . .

You may wish to solve the above puzzle yourself.

Here’s a 6x6 puzzle for Extensions 2. The solution is unique and deducible without guessing:

2 5 3 5 . 3

1 4 1 3 1 2

. 6 3 3 4 2

2 . 2 . 5 4

. 5 1 3 . 2

5 . 3 5 3 .

You may wish to solve the above puzzle yourself.

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• From James Dow Allen@21:1/5 to Steven Meyers on Sat Jan 11 10:53:25 2020
On Friday, January 10, 2020 at 4:35:02 AM UTC+7, Steven Meyers wrote:
Hello everyone,

Below is a write-up for my new puzzle, called Extensions.
Any and all feedback is welcome.

Congratulations! I did enjoy solving a few of the examples.
I think it must be difficult to design such a game. Well done!

You'll probably want a Javascript (or something) so people can play online.

The competition is ferocious, I'm afraid.
Simon Tatham has several puzzles online:
https://www.chiark.greenend.org.uk/~sgtatham/puzzles/
Of these I've tried and enjoy Towers, Untangle, Tent.
(I wrote a Black Box game 40 years ago!)

I like Tatham's Net, but play it at this site where it's called Circuits:
https://circuits.puzzlebaron.com/
Nurikabe is one of my favorites, but the puzzles at this site:
http://fabpedigree.com/nurikabe/
are too difficult. :-(

All of these, along with yours, Steven, are much more fun than
Sudoku, in my opinion.

Best wishes,
James Dow Allen (at Gmail)

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• From Steven Meyers@21:1/5 to James Dow Allen on Sat Jan 11 17:46:41 2020
On Saturday, January 11, 2020 at 1:53:27 PM UTC-5, James Dow Allen wrote:
On Friday, January 10, 2020 at 4:35:02 AM UTC+7, Steven Meyers wrote:
Hello everyone,

Below is a write-up for my new puzzle, called Extensions.
Any and all feedback is welcome.

Congratulations! I did enjoy solving a few of the examples.
I think it must be difficult to design such a game. Well done!

You'll probably want a Javascript (or something) so people can play online.

The competition is ferocious, I'm afraid.
Simon Tatham has several puzzles online:
https://www.chiark.greenend.org.uk/~sgtatham/puzzles/
Of these I've tried and enjoy Towers, Untangle, Tent.
(I wrote a Black Box game 40 years ago!)

I like Tatham's Net, but play it at this site where it's called Circuits:
https://circuits.puzzlebaron.com/
Nurikabe is one of my favorites, but the puzzles at this site:
http://fabpedigree.com/nurikabe/
are too difficult. :-(

All of these, along with yours, Steven, are much more fun than
Sudoku, in my opinion.

Best wishes,
James Dow Allen (at Gmail)

I'm glad that you like Extensions, that's encouraging to hear! I will look into the possibility of getting it programmed.

Thanks for the links, those are good. I enjoy Tents puzzles, and I admire Nurikabe a lot --- I think its design makes for inherently difficult puzzles.

Steve

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