Board Game Arena

For puzzle ID # C64 ASO I, how is verifier E essential? I believe I am able to find the correct answer even when verifier E is removed. What value, other than the correct answer, is valid when verifier E is omitted?

https://boardgamearena.com/archive/repl ... s=84207926;

So you have a pair and one even. So the odd number is present twice.
The sum is >6.

Then let's said that b<=bp. (it's possible that p<=by, if that's the case, swap b and p for all the remaining of this post)
If B is even then you got 233 255 455 as solutions
If B is odd then you got 334 343 as solutions.

So with ABCF you got five solutions: 233 255 455 334 343.
455 is impossible from D.

If b<4, then E will be the only one who can change those 4 solutions into 1: which is not possible.
So from your game, D then said that p<4. Which mean we can remove 255 334 and 455.

So with ABCDF, you got two solutions: 233 and 343 (since if b<4 two lines above then you got more than one final solution)[edit: that sentence is maybe wrong, but for that game that doesn't matter].
E tell you that y>3, and so you only have 343 left.

Thank you for the detailed response.

By using a test code of 353, I was able to confirm that b<=yp and p<=by, implying that b=p. Knowing that b=p, I was able to eliminate 233 as an option without using E.

Was my reasoning valid or am I missing something?

Timmy Thumb wrote: ↑19 March 2024, 21:31 Thank you for the detailed response.

By using a test code of 353, I was able to confirm that b<=yp and p<=by, implying that b=p. Knowing that b=p, I was able to eliminate 233 as an option without using E.

Was my reasoning valid or am I missing something?

F knows only that Bl is smallest/joint smallest. It knows *nothing* else about Y or P. F giving you a for 353 does NOT tell you that P=Bl. It would give you a for *any* code that has Bl smallest/joint smallest and a for *any* code where Bl is not smallest/joint smallest.

Read up on the X Paradox if you don't understand this point.

Thank you for the clarification. I understand the meaning of the card now. The wording is ambiguous, but I understand the need to be concise due to the space on the card. I believe the wording below is easier to understand:

This verifier verifies:
which color has the smallest number (or, in the case of a tie, it will verify only one of the colors that is tied for lowest)

It would be helpful to have a resource that provides a detailed explanation for the more complex cards.

The important take-away for the "Hard" criteria cards is that each verifier is only verifying one of the criteria listed on the card, and your task is to work out what each verifier knows rather than to find the final code. Once you know what each verifier knows, only one code will satisfy them all.

The hard verifiers are non-exclusive, so more than one listed fact might actually be true for the final code, but the verifier will not know that as it does not know the final code. It just knows its one fact, and all its answers will be related only to that one fact.

As long as you're aware of this, you won't over-interpret what a or means.