# What is the maximum number of statements that can be true?

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There are hundred statements which go as follows;

Statement 1: At least one of these statements is false.

Statement 2: At least two of these statements are false.

Statement 3: At least three of these statements are false.

Statement 4: At least four of these statements are false.

Statement 100: At least a hundred of these statements are false.

What is the maximum number of statements that can be true?

posted Feb 20
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## 2 Answers

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50 statements
.
In that case statement 1-50 are true (for a total of 50 statements)
and statement 51-100 are false (for a total of 50 statements).
So statement 50 (at least 50 statements are false) would be true,
but statement 51 (at least 51 statements are false) would be false.

answer Feb 20 by
–1 vote

100 statements that can be true.

answer Feb 27
If 100 statements are true, then all statements are true. Then how can the 100th statement (at least 100 of these statements are false) be true?

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