Btw, that problem is a good test for one’s “working memory” (very short term memory). If the working memory is having troubles, concentration becomes very difficult and one tends to feel impatient and look for the easy way out of problems (jump to a conclusion), sometimes at the expense of failure and/or frustration. It is caused by a chemical imbalance, usually the result of early viral infections that led to a series of neurological sensitivities and subtle anxiety.
100 pessimists have written 100 senntences on a sheet of paper. Each pessimist has written 1 sentence. The 100 sentences are numbered from 1 to 100. The first pessimist has written: “Exactly one sentence on this sheet is wrong.”. The second pessimist has written: “Exactly two sentences on this sheet are wrong.”. … And so on. Which sentences are wrong, which right?
You know from the text that they are 100 pessimists, that they have written 100 sentences, and that each of these 100 pessimists has written one sentence.
[tab]So you should refer to the time after all sentences were written; but if you refered to both the time of the writing and the time after all sentences were written, then it would also be correct. The latter is more important, or, in other words, you just have to and would probably almost automatically consider the time after all sentences were written.[/tab]
[tab]if dude x says exactly x sentences are wrong, and we are to take the opposite of what he says, them there are 3 alternatives
exactly x sentences are NOT wrong
NOT exactly x sentences are NOT wrong
NOT exactly x sentences are wrong
of the three, only the first one is determinable, since removing the exact portion makes the result indeterminable
so I’m going to go with all sentences are correct[/tab]
No. It isn’t false, merely not what you were intending. And in that case, the sentences being irrational, I have no idea what imaginary answer you would be looking for.
Three ladies gather for a meeting: Mrs. Red, Mrs. White, and Mrs. Green. One of the ladies says: “That’s strange, one of us is wearing a red, another one a white, and the third one a green blouse”. “This is really amazing”, said the lady with the red blouse, “because no one of us is wearing the blouse which corresponds to her name”. “That’s right”, Mrs. White adds.
[tab]The lady with the read blouse said that no one is wearing name macching colored blouse. It implies that lady must me either Mrs green or Mrs white. But, the next statement tells that she is not Mrs white but different. Thus, it confirms that Mrs Green is wearing red blouse. Now, as per first statement, we akready know that Mrs white is not wearing the red blouse, and she cannot wear white blose either, thus she must be wearing green blouse. Now, we have only one combintion left; Mrs red - white blouse.[/tab]
[tab]the woman wearing red is not mrs. white because mrs white is the one replying to her, and can’t be mrs. red because her color doesn’t match the name, therefore the woman wearing red is mrs. green.[/tab]
If you provide such a language, which cannot be interpreted in a way other that what you intended, you will get the right answer too, most of the times, at least.
Do you believe that the statement, “This statement is false” is a valid statement? Either true or false?
It is not. It is an irrational, self-contradicting, statement.
The statement “Every sentence on this page is wrong”, when there is only one statement on the page is the same as the above statement, irrational and self-contradicting, and thus neither true or false, but rather irrational.
===========================
After all of the statements have been written, the rationality of the statements changes because each statement had referred to only the statements that were already written at the time that they each were written, but after all of them are written, each statement encompasses all statements.
That is why I asked to which time you were referring, before all were written or after.
[tab]After they are all written only the last statement, 100th, is self-contradicting and thus irrational (not wrong). For it to be right, all statements have to be wrong including itself. The other statements assert that some of the statements, possibly other than themselves, are false/wrong, but they claim an exact amount of wrong statements.
The statement claiming 99 wrong statements would be either including itself, making it irrational, or including the 100th statement that is irrational. If it includes the 100th, it is wrong for claiming an irrational statement as being wrong. And if the other statements are also wrong, there would be 99 wrong statements with 1 irrational statement. And that would make the 99th statement right because it wasn’t including the irrational statement but rather itself. And then it being right would make it wrong again, and thus actually irrational. So the 99th is either wrong or irrational depending on whether the lesser statements are wrong.
If the 98th statement turned out to be wrong, it would cause the 99th statement to be irrational, but that would make itself irrational and thus turn the 99th to be wrong. And if the 99th is wrong as well as the lesser 97 statements, the 98th would turned out to be right. If the 98th is right, the 99th is definitely wrong (with 98 wrong and 1 irrational).
For the 97th to be right, the 96 lesser statements must be wrong as well as only one of those above it, such as the 99th. But the 98th depends upon the 97th to be wrong, thus if the 97th was right, the 98th would be wrong. And that would make two above the 97th wrong … one too many. And that demands that the 97th be wrong, which returns the 98th to being right.
The 96th requires that all lesser be wrong and only one above it being wrong. But there are already 2 above it that are wrong; 97th and 99th. That makes the 96th wrong already. And it being wrong allows the others above it to remain as they were.
From there on down to the first statement, each will have to be wrong for that same reason - too many above it are wrong and thus it must be wrong also.
============================
So in the long run, after all of the statements are written, only the 98th can be right in claiming that there are exactly 98 wrong statements (with one irrational).[/tab]
The riddles have different degrees of difficulty. They belong to different levels of difficulty.
Here they are again:
The Bridge.
Three Hidden Philosophers.
Three Light Switches.
Two Liars.
100 Pessimists.
Three Ladies.
Those six riddles have different degrees of difficulty, belong to different levels of difficulty. We can use the following degrees and levels of difficulty:
The riddle you solved, Zinnat, was one of the low level (degrees: 3 and 4). So it was a relatively easy riddle (I would say one of the degree 3). Riddles have their degrees of difficulty and belong to different levels of difficulty, Zinnat.
