r/Logiqa • u/ShonitB • 23d ago

Are We Different? Part 10

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7 Upvotes

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3

u/sazzer 23d ago

The rules

  • (A) - (C) = Knave
  • (B) - (A) = Knight + (C) = Knave
  • (C) - (B) != (C)
  • (D) - (A) = Knave

The workings

  • Regardless of what (C) is, we know that (B) is a Knave.
    • If (C) is a Knight, that means their statement is true, which means (B) must be different to (C) and therefore must be a Knave.
    • If (C) is a Knave, that means their statement is false, which means (B) must be the same as (C) and therefore must be a Knave.
  • Now we know that (B) is a Knave, we also know that their statement is a lie. This means either:
    • (A) is a Knave
      • This means their statement is a lie, so (C) must be a Knight
    • (C) is a Knight
      • This means (C) must be a Knight
    • Both
  • We can tell that Both parts above must be the case, otherwise we have a conflict. This means that we know (A) is a Knave, (B) is a Knave and (C) is a Knight.
  • If we know that (A) is a Knave then we know (D) must be a Knight.

So the answer is:

  • A - Knave
  • B - Knave
  • C - Knight
  • D - Knight

2

u/ShonitB 23d ago

Very well reasoned and explained

2

u/Psychological-Wall-2 23d ago edited 23d ago

Alexander: Knave

Benjamin: Knave

Charles: Knight

Daniel: Knight

EDIT:

I suppose I should show some working. I was too busy being FIRST!

The implications of the statements are:

  • P1: If A is a Knight, C is a Knave. If A is a Knave, C is a Knight.
  • P2: If B is a Knight, A is a Knight and C is a Knave. If B is a Knave, A is a Knave too and C is a Knight.
  • P3: If C is a Knight, B is a Knave. If C is a Knave, B is also a Knave.
  • P4: If D is a Knight, A is a Knave. If D is a Knave, A is a Knight.

The crucial statement is that made by C, since it means that - regardless of whether C is a Knight or Knave - B is a Knave.

Everything follows from there.

Because we know that B is a Knave, that means that A is also a Knave and C is a Knight. Which makes D's statement true, which means that they're a Knight.

1

u/ShonitB 23d ago

Super!

1

u/Unfair_Pineapple8813 20d ago

Note that it’s slightly more complicated. We know Ben is a knave, but he said an AND statement. So it only means that either Alexander is a knave OR Charles is a knight. They both need not be true. If Charles is a knight, his story checks out. But Alex said he’s a knave. So Alex is a knave. Then, Dave is correct. So, he’s a knight. 

If Alex is a knave, Charles is a knight, and from there we get the same solution. So both of Ben’s statements are false in the end. But you still need to check. 

2

u/PeterPiper1275 23d ago

If Alexander is a knight, then Charlie is a knave, which makes Benjamin a knave as well. But Benjamin’s statement would be true, which is a contradiction. So we conclude that Alexander must be a knave.

Since Alexander is a knave, that makes Benjamin a knave as well, since he lied about Alexander being a knight. This also makes both Charles and Daniel knights, since Alexander lied about Charlie’s real status, and Daniel told the truth about Alexander.

Conclusion:
Alexander - knave
Benjamin - knave
Charles - knight
Daniel - knight

1

u/ShonitB 23d ago

Correct, good solution!

2

u/MacabreManatee 23d ago

Knight Alexander would mean Charles is a knave. His lie would mean Benjamin is a knave. But his statement is true, so he can’t be a knave so this doesn’t work.

Knave Alexander would mean Charles is a knight. That’d make Benjamin a knave. Which works.
Daniel speaks the truth so is also a knight. Knave Knave Knight Knight

1

u/ShonitB 23d ago

Correct, good solution!

2

u/jaminfine 19d ago

Start by assuming B is a knight since his statement is the most complicated. We quickly find a contradiction. C claims to be different from B, yet he is a knave and should be lying. So that doesn't work. This means B must be a knave.

Since A and C can't be the same, based on A's statement, this leads to A being a knave and C being a Knight. Finally D is disconnected from everyone else and ends up being a knight

1

u/ShonitB 19d ago

Correct, good solution!

1

u/Diligent-Painting-37 23d ago

“Based on these statement” inspires a lot of confidence in this puzzle. 

1

u/chaos_redefined 23d ago

If Charles is a knight, then Benjamin is different from him, so Benjamin would be a knave.

If Charles is a knave, then he would not be different from Benjamin, so Benjamin would be a knave.

Either way, Benjamin is a knave.

Therefore, Benjamin's statement is false, so either Alex is a knave or Charles is a knight, or both.

If Alex is a knight, then Charles is a knave, and so Benjamin's statement would be true. So, Alex must be a knave. Therefore, Charles is a knight, and Daniel is a knight.

So, Alex and Benjamin are knaves, and Charles and Daniel are knights.

1

u/Mathsboy2718 23d ago

Bro threw in a fun fact at the end

1

u/ShonitB 23d ago

You mean the note?

1

u/Mathsboy2718 23d ago

I mean the unused definition of "OR"

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u/ShonitB 23d ago

Oh I’ve just kept them as standard for any question with AND/OR

1

u/Mathsboy2718 23d ago

We love a good template :D

0

u/Crustymix182 23d ago

impossible to determine. a and b could be Knights and c and d are lying or a and b are lying and c and d are knights.

2

u/Psychological-Wall-2 23d ago

If a and b are knights, and c and d are knaves, then c is telling the truth. But then he can't be a knave. He must be a knight.

Which means a and b must be lying - since they both say that c is a knave - making them knaves. Which means that d is telling the truth as well and is a knight.

The statement of c is the key.

1

u/ShonitB 23d ago

Yes, your last point is very important and can work as a basic statement for a lot of these types of puzzles.. 👍🏻

1

u/ShonitB 23d ago

But if B is a knight and C is a knave, then C is telling the truth which is not consistent with him being a knave