Hi Roppo,
This is an advanced linear game. The base will be the order 1-5, the bottom row will be the commercials (F, G, H, I, and K) and the top row will be for the short/long (S/L) distinction.
Because we're setting up the long/short variables on the top row, the first rule gives us two vertical blocks.
[L] [L]
[G] [K]
(Note - These two blocks would usually have boxes around them to visually represent the blocks. I'm using brackets here to simulate a box.)
The second rule tells us that the 3rd commercial is Long, so we will add that into our main diagram below.
The third rule tells us that Long commercials cannot be consecutive, which we would diagram as a horizontal not block.
[L / L]
(Note that it is perfectly fine for two Short commercials to go next to each other.)
The final rules combines both a sequencing rule and a block
I - [HK}
(I is before the HK block)
(Note that F is a random.)
Inferences
Because Long commercials cannot be consecutive and the 3rd commercial is long, the 2nd and 4th commercial must be short.
Because K appears in both rule 1 and 4, we can link these rules to expand on our sequence/block.
[L]
I - [HK]
The main diagram looks like:
___
_S_
_L_
_S_
___
___
___
___
___
___
1
2
3
4
5
H K I I
K G G H
K
(Note - below the diagram are the Not Laws showing where certain variables cannot go. The G and K Not Laws in 2 and 4 are because G and and K are Long commercials, but 2 and 4 are Short commercials. The other Not Laws come from the final rule.)
The key inference is that K can only go space 3 or space 5. This fundamental divide is what suggest using templates based on each of those options.
Temp 1 (K in 3)
___
_S_
_L_
_S_
_L_
I
H
K
F
G
___
___
___
___
___
1
2
3
4
5
(Note - When K is 3, it forces I in 1 and H in 2 as those are the only available spaces to fit them. At that point, G which is a Long commercial, must go in 5, and F goes into 4 by process of elimination. The only uncertainty in this template is whether the first commercial is Long or Short.)
Temp 2 (K in 5)
___
_S_
_L_
_S_
_L_
G/
/G
H
K
___
___
___
___
___
1
2
3
4
5
(Note - When K is 5, we know that the 5th commercial is Long since K is always Long from rule 1. We also know that H must go in 4 because [HK] form a block from rule 4. We know that G must go either 1 or 3 at this point as those are the only remaining spaces that could be Long. We can show this as a split dual option shown above.)
Those are the two templates that capture the two major branches of the game.
The individual questions to the game will be answered separately under those Topic Headings.
