JohnnyCyclops wrote: ↑09 January 2024, 22:36
poptasticboy wrote: ↑09 January 2024, 20:54
JohnnyCyclops wrote: ↑09 January 2024, 20:32
To learn from the better players I looked at a game you played earlier today.
https://boardgamearena.com/gamereview?table=459919171
I see you went straight to the answer without a single test, 252, but I can't see why 242 couldn't also be a true answer, assuming the yellow square has to be the largest value. Without a single test, say to determine whether the yellow sqaure is odd/even, how did you land on 252 not 242 please?
So if there were more Evens, Bl=P and Y Even, then verifier C (number of 3s) would be redundant.
Thank you for replying. I'm sure it makes sense and I'm just not grasping it. Verifier C would still be used, but would return "no 3s" for the answer 252, but also "no 3s" if 242 was an answer. I could see using Verifier B (is Y odd/even) would allow you to confirm it was a 5 thus 252, but without testing that one I can't see any other clue in the verifiers that would say Y couldn't also be a 4.
No verifier can be redundant in a valid puzzle.
If the answer to this puzzle were 242, you would have "More Evens", "Yellow Even" and "Blue=Purple" as true. However, in these circumstances all three colours would have to be Even. This would mean that the "Number of 3s" verifier would provide no additional information and so would be redundant.
This is not possible in a valid puzzle; every single verifier must be necessary to find the solution. So if a certain subset of verifier responses would mean that another verifier would provide no new information, that combination is impossible.
So the combination "More Evens", "Yellow Even" and "Blue=Purple" is not valid, as it would make "number of 3s" useless.
If you still can't see it, try it this way. Imagine that 242 was correct and the verifiers all have the correct answers for that solution. Now remove the "Number of 3s" verifier completely, but leave the other Verifiers giving the same answers.
Using just those 5 Verifiers, you would still reach the unique answer 242. The "number of 3s" verifier did not need to be used at all to reach the answer.
This tells you that that can not possibly be the correct solution.