This is a fascinating logic puzzle that requires careful, step-by-step deduction. Let's break down the clues to find the solution.

First, let's translate each clue into a clear logical statement.

1. Clue 1: "The delivery will not arrive on a Monday."

   This is a direct exclusion. The day is not Monday.

2. Clue 2: "If the delivery arrives before Thursday, then it must arrive on a Wednesday."

   • This is a conditional statement. Let's represent it as: If (Day is Monday, Tuesday, or Wednesday), then (Day is Wednesday).
   • A key principle of logic is that if the "if" part of a statement is false, the entire statement is considered true (it's called a vacuous truth). For example, "If the sky is green, then I am a billionaire" is a true statement because the sky is not green. Applying this, if the delivery day is Thursday, Friday, Saturday, or Sunday, the condition "arrives before Thursday" is false, so the clue is not violated.

3. Clue 3: "The delivery will arrive after the day that comes immediately after Monday."

   • Let's simplify this. The day that comes immediately after Monday is Tuesday.
   • Therefore, this clue means: The delivery will arrive after Tuesday.
   • This narrows the possibilities to: Wednesday, Thursday, Friday, Saturday, or Sunday.

4. Clue 4: "The delivery will not arrive on a Friday."

   This is another direct exclusion. The day is not Friday.

Step-by-Step Deduction

Now, let's combine these clues to find the exact day.

1. Start with the most restrictive clue. Clue 3 gives us a strong starting point by defining a range of possible days.

   • From Clue 3, the possible days are: Wednesday, Thursday, Friday, Saturday, Sunday.

2. Apply the exclusions. We can now use Clue 1 and Clue 4 to eliminate days from our list.

   • Clue 1 says it's not Monday (already excluded).
   • Clue 4 says it's not Friday.
   • Our list of possible days is now reduced to: Wednesday, Thursday, Saturday, Sunday.

3. Analyze the conditional clue. Now we must evaluate Clue 2 against our remaining possibilities: "If the delivery arrives before Thursday, then it must arrive on a Wednesday."

   • Let's test each remaining day:
     • Wednesday: Does this work? Yes. The condition "arrives before Thursday" is true (Wednesday is before Thursday), and the result "arrives on a Wednesday" is also true. The statement holds.
     • Thursday: Does this work? Yes. The condition "arrives before Thursday" is false. As explained in the analysis, when the "if" part is false, the entire statement is logically true. This clue does not exclude Thursday.
     • Saturday: Does this work? Yes. The condition "arrives before Thursday" is false. The statement is logically true and does not exclude Saturday.
     • Sunday: Does this work? Yes. The condition "arrives before Thursday" is false. The statement is logically true and does not exclude Sunday.

Conclusion

After a rigorous, step-by-step analysis of all four clues, we are left with four possible days that satisfy all the given conditions: Wednesday, Thursday, Saturday, and Sunday.

While this result may seem ambiguous for a logic puzzle, it is the only conclusion supported by the text. The clues, as written, do not provide enough information to narrow the choice down to a single day. The "hidden" element of this puzzle is that it reveals a potential flaw or ambiguity in the setup, demonstrating that not all logical problems have a single, unique solution.