Thanks to andycivil, who solved Glimmer and Gloom on Very Hard. He posted in the comments section of his solution video of a way to complete it by memory. I wanted to share with you all. https://www.youtube.com/watch?v=q5Cr9QSZiu0
There are five solutions to Very Hard, as opposed to 511 (777 in octal!) To use this guide, I recommend having played Glimmer and Gloom before. Using rotational symmetry and superposition, I hope to show you a whole new world. I will also attempt to teach you octal notation if you don't already know it. This isn't a math guide. There is no math here. I know, cause andy said he's not a math guy.
Link to Glimmer and Gloom in Fairgrounds
Guide
To win the game, change all tiles to a single color.
To begin, clear the game board by clicking the tile down and to the right of each "active" tile. This being dark tiles if you solve for light, and vice versa.
Afterwards you will have from 1 to 9 active tiles remaining on the bottom and bottom-right edges. This will be our "output row." It is very important that no other active tiles remain elsewhere on the board.
From left to right, I will be referring to these tiles as "output 1-9."
The bottom row of 5 tiles, tiles 1-5, can be cleared individually by a specific combination of clicks in the "input row," the tiles on the top-left and top edges of the board.
The tiles going along the bottom-right edge, tiles 6-9, excluding the corner tile 5 at the bottom, can be cleared using the same combinations mirrored. These will be patterns 4 to 1, clicking the input row from right-to-left, instead of left-to-right. For tile 6, use mirrored pattern 4. For tile 9, use mirrored pattern 1.
Memorize these patterns:
1: 000 101 001
2: 000 011 110
3: 001 101 010
4: 101 101 111
5: 010 010 010
For each "1" in the pattern, click the corresponding tile in the input row (the 9 tiles on the top-left and top edges of the board). If your output row has more than one active tile, you will need to superimpose the patterns for each of them. Once you get to tiles 6 and onward, use the patterns 4, 3, 2 and 1, except mirrored-- that is, use the same sequences except from right-to-left.
To be clear, these are the mirrored patterns:
6/4: 111 101 101
7/3: 010 101 100
8/2: 011 110 000
9/1: 100 101 000
If you find these sequences are too long to memorize, keep reading to the section on octal.
For a visual guide to the inputs, CenedraRiva posted these images.
Diagram of the board, with input and output rows labeled.
Octal: A shortcut to memorization
Learning octal notation, or base-8 numerals, can be a shortcut to memorizing the solutions. As each 9-digit pattern is condensed into 3 digits, it feels a little less like memorizing a phone book. If you already have knowledge of binary, learning octal is a breeze, and if not... try it!
The patterns, converted to octal:
1: 051
2: 036
3: 152
4: 557
5: 222
How to Octal:
3 binary digits (we'll call it a triplet) can be expressed as an octal digit from 0 to 7. 000, 001, 010, 011, 100, 101, 110, 111.
This way, a string of 9 binary digits is shortened to a manageable 3 digits. When you get the hang of it, converting binary to octal on the fly is a piece of cake.
In a binary triplet, the rightmost digit is the ones place. The middle digit is the twos place. The left digit is the fours place. You can sum these to quickly convert binary to octal.
The short version of binary to octal conversions:
100 = 4
10 = 2
1 = 1
Sum these together as needed.
Note on the mirrored patterns:
By entering your input patterns from right-to-left, there shouldn't be any problems here, but I should mention that the octal sequences mirrored are not equivalent to the same digits in reverse order. Pattern 1 (051) is the binary sequence 000 101 001. Mirrored, this is 100 101 000. Converting this to octal, we get 450. Had we entered the octal sequence 150 we would be in trouble, so don't do it.
For a cheatsheet to the mirrored inputs in octal, 3ctoplasm posted this image.
andycivil's comment that sparked this guide:
Other Links
sQld's G&G Very Hard Ultimate Solver- The improved G&G Very Hard tool. I recommend this!
JumboDS64's guide to G&G Very Hard. There are useful strategies in the replies to this thread as well. Try this alphabet mnemonic (illustrated)
Catradora's guide to G&G Very Hard (Has pictures)
Paladingineer's guide and their Troubleshooting guide. With pictures!
Chatoyant's guide. Has pictures
Not a guide to Very Hard, but rather Hard mode: Mahogi's guide. Also has pictures!
*NEW* CenedraRiva's G&G Very Hard visual guide
If one strategy doesn't work, try another. The benefits of success are too great to give up trying.
If you have questions, comments, or suggestions feel free to reply in this thread. Especially if you can offer images to accompany the text ^_^ Additionally, anyone is welcome to share, adapt or improve my words. Thanks for reading.
Edit 11/14/2021: Shunted the octal sequences underneath their own separate subheader. Also added a diagram of the input and output rows' locations.
There are five solutions to Very Hard, as opposed to 511 (777 in octal!) To use this guide, I recommend having played Glimmer and Gloom before. Using rotational symmetry and superposition, I hope to show you a whole new world. I will also attempt to teach you octal notation if you don't already know it. This isn't a math guide. There is no math here. I know, cause andy said he's not a math guy.
Link to Glimmer and Gloom in Fairgrounds
Guide
To win the game, change all tiles to a single color.
To begin, clear the game board by clicking the tile down and to the right of each "active" tile. This being dark tiles if you solve for light, and vice versa.
Afterwards you will have from 1 to 9 active tiles remaining on the bottom and bottom-right edges. This will be our "output row." It is very important that no other active tiles remain elsewhere on the board.
From left to right, I will be referring to these tiles as "output 1-9."
The bottom row of 5 tiles, tiles 1-5, can be cleared individually by a specific combination of clicks in the "input row," the tiles on the top-left and top edges of the board.
The tiles going along the bottom-right edge, tiles 6-9, excluding the corner tile 5 at the bottom, can be cleared using the same combinations mirrored. These will be patterns 4 to 1, clicking the input row from right-to-left, instead of left-to-right. For tile 6, use mirrored pattern 4. For tile 9, use mirrored pattern 1.
Memorize these patterns:
1: 000 101 001
2: 000 011 110
3: 001 101 010
4: 101 101 111
5: 010 010 010
For each "1" in the pattern, click the corresponding tile in the input row (the 9 tiles on the top-left and top edges of the board). If your output row has more than one active tile, you will need to superimpose the patterns for each of them. Once you get to tiles 6 and onward, use the patterns 4, 3, 2 and 1, except mirrored-- that is, use the same sequences except from right-to-left.
To be clear, these are the mirrored patterns:
6/4: 111 101 101
7/3: 010 101 100
8/2: 011 110 000
9/1: 100 101 000
If you find these sequences are too long to memorize, keep reading to the section on octal.
For a visual guide to the inputs, CenedraRiva posted these images.
Diagram of the board, with input and output rows labeled.
Octal: A shortcut to memorization
Learning octal notation, or base-8 numerals, can be a shortcut to memorizing the solutions. As each 9-digit pattern is condensed into 3 digits, it feels a little less like memorizing a phone book. If you already have knowledge of binary, learning octal is a breeze, and if not... try it!
The patterns, converted to octal:
1: 051
2: 036
3: 152
4: 557
5: 222
How to Octal:
3 binary digits (we'll call it a triplet) can be expressed as an octal digit from 0 to 7. 000, 001, 010, 011, 100, 101, 110, 111.
This way, a string of 9 binary digits is shortened to a manageable 3 digits. When you get the hang of it, converting binary to octal on the fly is a piece of cake.
In a binary triplet, the rightmost digit is the ones place. The middle digit is the twos place. The left digit is the fours place. You can sum these to quickly convert binary to octal.
The short version of binary to octal conversions:
100 = 4
10 = 2
1 = 1
Sum these together as needed.
Note on the mirrored patterns:
By entering your input patterns from right-to-left, there shouldn't be any problems here, but I should mention that the octal sequences mirrored are not equivalent to the same digits in reverse order. Pattern 1 (051) is the binary sequence 000 101 001. Mirrored, this is 100 101 000. Converting this to octal, we get 450. Had we entered the octal sequence 150 we would be in trouble, so don't do it.
For a cheatsheet to the mirrored inputs in octal, 3ctoplasm posted this image.
andycivil's comment that sparked this guide:
Quote:
How to solve the puzzle if you want to memorise it.
You have to understand octal notation. The top, and top left rows are defined as INPUTs. The bottom, and bottom right rows are defined as OUTPUTs.
You can save on memory by using SUPERPOSITION and ROTATIONAL SYMMETRY. This way, you only need to remember the patterns for 20 (=222), 10 (=557), 4 (=152), 2 (=36) and 1 (=51). That's it.
This is how you do it. Clear the board until only output tiles are active. Now apply inputs, one pattern for each active output tile. First, read counter-clockwise from the middle output tile. e.g. if the bottom right tile is active, apply COUNTERCLOCKWISE the bit pattern 222 to the input tiles as clicks. (Click the correct three tiles.) Now, continue counter-clockwise, wherever an output tile is active, apply the pattern from the table, in a counter-clockwise direction. Now, do the other output tiles in a CLOCKWISE direction. Don't re-do the bottom right tile (20) because you've already done it. Start from 10, the first tile you didn't do yet.
Where you find an active tile, apply the SAME pattern to the input tiles, but in a CLOCKWISE direction. When you're applying each of these patterns, you must IGNORE the current state of the input tiles - you're just blindly applying a pattern of clicks. If you don't understand why the octal number 557 represents seven clicks, you'll never get this. When you have applied an input click-pattern for every active output tile, you can clear the board again and it should be done. This method is slower, but you can at least do it 'unaided' if you want a party trick to impress your friends.
You have to understand octal notation. The top, and top left rows are defined as INPUTs. The bottom, and bottom right rows are defined as OUTPUTs.
You can save on memory by using SUPERPOSITION and ROTATIONAL SYMMETRY. This way, you only need to remember the patterns for 20 (=222), 10 (=557), 4 (=152), 2 (=36) and 1 (=51). That's it.
This is how you do it. Clear the board until only output tiles are active. Now apply inputs, one pattern for each active output tile. First, read counter-clockwise from the middle output tile. e.g. if the bottom right tile is active, apply COUNTERCLOCKWISE the bit pattern 222 to the input tiles as clicks. (Click the correct three tiles.) Now, continue counter-clockwise, wherever an output tile is active, apply the pattern from the table, in a counter-clockwise direction. Now, do the other output tiles in a CLOCKWISE direction. Don't re-do the bottom right tile (20) because you've already done it. Start from 10, the first tile you didn't do yet.
Where you find an active tile, apply the SAME pattern to the input tiles, but in a CLOCKWISE direction. When you're applying each of these patterns, you must IGNORE the current state of the input tiles - you're just blindly applying a pattern of clicks. If you don't understand why the octal number 557 represents seven clicks, you'll never get this. When you have applied an input click-pattern for every active output tile, you can clear the board again and it should be done. This method is slower, but you can at least do it 'unaided' if you want a party trick to impress your friends.
Other Links
sQld's G&G Very Hard Ultimate Solver- The improved G&G Very Hard tool. I recommend this!
JumboDS64's guide to G&G Very Hard. There are useful strategies in the replies to this thread as well. Try this alphabet mnemonic (illustrated)
Catradora's guide to G&G Very Hard (Has pictures)
Paladingineer's guide and their Troubleshooting guide. With pictures!
Chatoyant's guide. Has pictures
Not a guide to Very Hard, but rather Hard mode: Mahogi's guide. Also has pictures!
*NEW* CenedraRiva's G&G Very Hard visual guide
If one strategy doesn't work, try another. The benefits of success are too great to give up trying.
If you have questions, comments, or suggestions feel free to reply in this thread. Especially if you can offer images to accompany the text ^_^ Additionally, anyone is welcome to share, adapt or improve my words. Thanks for reading.
Edit 11/14/2021: Shunted the octal sequences underneath their own separate subheader. Also added a diagram of the input and output rows' locations.
Bone Friend wanted.
Dragons for Sale!
Glimmer and Gloom Very Hard: Memorize it!
I'm sure other people will get a lot out of this.
