Reasoned for 3m 42s
Reasoned for 3m 42s I’m looking at how the Set game cards are represented in shorthand. The notation goes: [Shape][Number][Color][Shading].
For example, “O2RS” means an Oval (O), 2 of them, in Red (R), Solid shading (S). So far, so good.
Now with “O1PH,” I see it’s an Oval (O), 1 of them, in Purple (P), with Hashed shading (H). I’m just double-checking the consistency of the shading description, since “hashed” is noted as H. It’s a little tricky, but I think I have it!
Looking at card 7, “D3GO” is shorthand for Diamond, 3, Green, Outlined. But the description says “Two outlined green diamonds,” which doesn’t match. Hmm, the shorthand seems clearer than the description, so I’ll trust that. It’s likely a mistake in the description.
I’ll check card 8, and it has the same issue: “S3GO” means Squiggle, 3, Green, Outlined, but the description says “Two outlined.” This pattern suggests descriptions are inconsistent, but shorthand is probably correct. I’ll stick with the shorthand interpretation for now.
I’m going with shorthand as the reliable format. For example, card 7 is Diamond, 3, Green, and Outlined; card 8 is Squiggle, 3, Green, Outlined.
Now I’ve listed out all the cards with attributes: Shape, Number, Color, Shading. Each attribute has three possible values, leading to many combinations. To find sets, I’ll look for combinations of 3 cards where for each attribute, they are either all the same or all different.
I’ll try encoding the attributes to work systematically, using mod 3 for each. This will help me find valid sets.
It seems like I’m working through some validation checks to determine if these cards form a valid set. For each combination, I’m scrutinizing different aspects: shape, number, color, and shading.
It’s a tough task, but as I go through each group, I’ve determined if a set is valid or not based on whether the attributes are either completely different or the same. Some combinations I looked at are invalid due to mismatched properties.
At least I’m keeping track of the valid sets.
It looks like I’ve found several card combinations that work as sets, such as (2,6,7), (3,4,5), and (5,6,10). I’ve rechecked and confirmed these sets.
But I need to verify (8,9,12) — earlier, I thought this was a valid set, but when comparing the colors, it turns out to fail. The colors don’t match. However, the shading does, so I need to correct my initial assessment on this one.
I’ll keep those confirmed sets but remove (8,9,12) from the list.
Below are five valid Sets found in the layout:
• Card 2, Card 6, Card 7
• Card 3, Card 4, Card 5
• Card 5, Card 6, Card 10
• Card 5, Card 8, Card 12
• Card 10, Card 11, Card 12
Each Set meets the rule: for every attribute, the three cards are either all the same or all different.