Logical Riddle: What Is The Maximum Number Of Statements That Can Be True?
Use your logical skills to solve this riddle.
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?
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Answer: 50 statements are correct and 50 are incorrect. Statements 1 to 50 are true and statements 51 to 100 are false.
Explanation:
If any one of the statements is true, then all of the statements numbered lower than that one must also be true, because the term “at least” is inclusive of a fewer number, and they are numbered in ascending order.
Assuming statement 1 is true; then statement 100 is false.
Assuming statements 1-2 are true; then statements 99-100 are false.
Assuming statements 1-3 are true; then statements 98-100 are false.
Assuming statements 1-4 are true; then statements 97-100 are false.
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Assuming statements 1-50 are true; then statements 51-100 are false.
Statement 99 will be the only correct statement if the terms “at least” are replaced with the term “exactly.”, e.g. “Exactly 99 of these statements are false.”