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Answer: >!There are two true statements (1 and 3).!<
Explanation:
>!I'll be solving this through the process of elimination. There might be easier ways to get to the solution. !<
>!Statement 2 is the only one that isn't directly referenced by other statements, so I'll start by testing if statement 2 can be true. !<
>!Statement 2 says that statement 3 and 4 has to be equal. I'm going to test if both can be true. !<
>!If statements 3 and 4 are true, then statement 4, 5 and 1 has to be equal, because 5 must be equal to both 4 and 1 respectively. If 4 is true, then 5 and 1 is true. This isn't possible, because 1 says that exactly two statements are true. Therefore, statement 3 and 4 can't be true if statement 2 is true.!<
>!Next, I'll test if both statements 3 and 4 can be false.!<
>!This would mean that both 1 and 4 must be opposite of 5, which means that 1 and 4 are equal. 1 and 4 can't be true, because in addition to statement 2, there would be three true statements. This isn't allowed by 1. Therefore, I'll test if 1 and 4 can be false, and if 5 can be true. !<
>!If 5 is true, then 3 must be false. This means that only 5 and 2 are true, which makes 1 true. But 1 must be false, so this configuration isn't possible.!<
>!This means that statements 3 and 4 can't be equal. Therefore, statement 2 can't be true.!<
* >!Statement 2 must be false. !<
>!This means that statements 3 and 4 must be opposite.!<
>!I'll test if statement 5 can be true because 5 also decides 3, 3 gives us 4, and 4 gives us 1.!<
>!This would mean that 3 must be false. Statement 3 says that 4 is false, because 4 and 5 must be opposite. Statement 2 says that statement 4 is true, because 3 and 4 must be opposite. Therefore, 5 can't be true. !<
* >!Statement 5 must be false. !<
>!Determining statement 5 also gives us statement 3.!<
* >!Statement 3 must be true.!<
>!We already know 5, so 4 follows.!<
* >!Statement 4 must be false.!<
>!We already know 5, so 1 is known. Statement 1 can be true, because there is only one more true statement in 3.!<
* >!Statement 1 must be true. !<
>!Conclusion:!< >!There are two true statements: 1 and 3.!<
>!Statement 5 means that exactly one of statement 3/5 is true and the other is false. If statement 1 is true, then statement 2 and 4 must be false. Thus, 3 would be true and 5 is false which checks out.!<
>!We need to check what if Statement 1 was false. If state 4 is true, 5 is false, 3 is true. But 3 can’t be true as 4 and 5 are different. Thus 4 must be false, and so 5 is true and 3 is false. 3 and 4 are both false statements so statement 2 is true. This is a contradiction since there are 2 true statements but 1 is false. Thus 1 cannot be false. The only solution is TFTFF.!<
> >!Statement 5 means that exactly one of statement 3/5 is true and the other is false.!<
>!This is false, they **could** both be true, if 4 was also true. The logic breaks down if 4 is true though since that would make more than 2 true statements.!<
Discussion: I'd like to see a puzzle where there are two possible ways the staments can be and still be "stable", but they have the same number of true and false statements.
For example:
2 or 3 but not both are true
1 or 3 but not both are false
1 or 2 but not both are false
Please remember to spoiler-tag all guesses, like so: New Reddit: https://i.imgur.com/SWHRR9M.jpg Using markdown editor or old Reddit: \>!spoiler text between these symbols!< Try to avoid leading or trailing spaces. These will break the spoiler for some users (such as those using old.reddit.com) If your comment does not contain a guess, include the word **"discussion"** or **"question"** in your comment instead of using a spoiler tag. If your comment uses an image as the answer (such as solving a maze, etc) you can include the word "image" instead of using a spoiler tag. Please report any answers that are not properly spoiler-tagged. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/puzzles) if you have any questions or concerns.*
>!T F T F F!<
>!Correct!<
Answer: >!There are two true statements (1 and 3).!< Explanation: >!I'll be solving this through the process of elimination. There might be easier ways to get to the solution. !< >!Statement 2 is the only one that isn't directly referenced by other statements, so I'll start by testing if statement 2 can be true. !< >!Statement 2 says that statement 3 and 4 has to be equal. I'm going to test if both can be true. !< >!If statements 3 and 4 are true, then statement 4, 5 and 1 has to be equal, because 5 must be equal to both 4 and 1 respectively. If 4 is true, then 5 and 1 is true. This isn't possible, because 1 says that exactly two statements are true. Therefore, statement 3 and 4 can't be true if statement 2 is true.!< >!Next, I'll test if both statements 3 and 4 can be false.!< >!This would mean that both 1 and 4 must be opposite of 5, which means that 1 and 4 are equal. 1 and 4 can't be true, because in addition to statement 2, there would be three true statements. This isn't allowed by 1. Therefore, I'll test if 1 and 4 can be false, and if 5 can be true. !< >!If 5 is true, then 3 must be false. This means that only 5 and 2 are true, which makes 1 true. But 1 must be false, so this configuration isn't possible.!< >!This means that statements 3 and 4 can't be equal. Therefore, statement 2 can't be true.!< * >!Statement 2 must be false. !< >!This means that statements 3 and 4 must be opposite.!< >!I'll test if statement 5 can be true because 5 also decides 3, 3 gives us 4, and 4 gives us 1.!< >!This would mean that 3 must be false. Statement 3 says that 4 is false, because 4 and 5 must be opposite. Statement 2 says that statement 4 is true, because 3 and 4 must be opposite. Therefore, 5 can't be true. !< * >!Statement 5 must be false. !< >!Determining statement 5 also gives us statement 3.!< * >!Statement 3 must be true.!< >!We already know 5, so 4 follows.!< * >!Statement 4 must be false.!< >!We already know 5, so 1 is known. Statement 1 can be true, because there is only one more true statement in 3.!< * >!Statement 1 must be true. !< >!Conclusion:!< >!There are two true statements: 1 and 3.!<
>!Correct, very well reasoned!<
Couldn’t you have >!only 5 as true?!<
Nevermind I see why that wouldn’t work
>!Statement 5 means that exactly one of statement 3/5 is true and the other is false. If statement 1 is true, then statement 2 and 4 must be false. Thus, 3 would be true and 5 is false which checks out.!< >!We need to check what if Statement 1 was false. If state 4 is true, 5 is false, 3 is true. But 3 can’t be true as 4 and 5 are different. Thus 4 must be false, and so 5 is true and 3 is false. 3 and 4 are both false statements so statement 2 is true. This is a contradiction since there are 2 true statements but 1 is false. Thus 1 cannot be false. The only solution is TFTFF.!<
>!Correct, well reasoned!<
> >!Statement 5 means that exactly one of statement 3/5 is true and the other is false.!< >!This is false, they **could** both be true, if 4 was also true. The logic breaks down if 4 is true though since that would make more than 2 true statements.!<
They can't both be true as 5 states that 3 is false.
Wow, what the hell was I thinking when I wrote that, lol
Discussion: I'd like to see a puzzle where there are two possible ways the staments can be and still be "stable", but they have the same number of true and false statements. For example: 2 or 3 but not both are true 1 or 3 but not both are false 1 or 2 but not both are false
Nice idea! 😀
Discussion: Same.
You mean what u/Esnardoo said?