Logical Riddle: What Is The Maximum Number Of Statements That Can Be True?

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.
…
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.”