Variant on a Well-Known Card Puzzle

Question

This is a variant on a well-known logic puzzle. It is not intended to be difficult, given that we are now officially in the “silly season”. Yesterday I won first prize in a Chess tournament, only to discover someone forgot to put a cheque in my envelope. Today, I saw a driver who forgot to display his D-plates when driving home (D stands for a word that rhymes with “Thick Ed” and cannot be represented using Alphabetic String Theory for several reasons).

But I digress …

Standard Spider Solitaire rules apply. It is relatively straightforward to expose all the cards in the tableau without dealing the remaining 10 cards in the stock.

Consider the following statements

• Every hidden card that is directly underneath a Three of any suit (*) is a King

• Every hidden card that is directly underneath a Heart of any rank (*) is a King

• Every hidden card that is directly underneath a Three of any suit (*) is a Club

• Every hidden card that is directly underneath an Eight of any suit (*) is a Three

(*) Can be either exposed or hidden.

QUESTION: For each of the four statements above, what is the minimum number of face-down cards we must expose before we are certain to verify the correctness/falsehood of said statement?

For purposes of answering the question, assume that you cannot deal the remaining ten cards in the stock.

You must answer correctly for all four statements above to earn the checkmark. There will be no partial credit or feedback other than “at least one of your answers is wrong” 😊

Answer 1

I deleted my previous answer because I misunderstood some of the rules. Hopefully, this one is right!

Every hidden card that is directly underneath a Three of any suit is a King

The card under the five doesn't need to be flipped since it doesn't grant any useful information. There is one three and two kings left in the cards we don't see. Flipping the card under the visible three is sufficient to check if the sentence is true: it's either a king, so the sentence must be right because the second hidden card becomes irrelevant, or not a king and the sentence must be false.

Hence:

Only one card needs to be flipped.

Every hidden card that is directly underneath a Heart of any rank is a King

There is 6 hearts left hidden. We obviously need to check the card under the five of hearts to make sure it's a king. Now, we also need to flip the two others cards, to see if there's a heart under the three and to check if the card under it is indeed a king.

Hence:

Three cards needs to be flipped.

Every hidden card that is directly underneath a Three of any suit is a Club

The three of clubs is still hidden somewhere, and there is three more clubs hidden. The card under the five is irrelevant, but we still need to flip the two others cards, to see if there's the three of clubs under the three of diamonds and to check if the card under it is indeed a clubs.

Hence:

Two cards needs to be flipped.

Every hidden card that is directly underneath an Eight of any suit is a Three

All eights have already been dealt, and no hidden card is under an eight.

Hence:

The sentence is true and no card needs to be flipped.