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# Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 3, August 2022

2022-08-08

## X Sentences Are False

Which sentence is correct?

Two men have fun and write 100 sentences on a sheet of paper and number them from 1 to 100. The first sentence is: “Exactly one sentence on this sheet is false,” the second: “Exactly two sentences on this sheet are false,” and so on.

But which sentence is correct now?

## Solution

The sentences on the sheet all contradict each other. Each sentence gives a different number of sentences that are false. However, one of the sentences must be true, because sentence number 100 rules out the possibility that all the sentences are false—it would be true that 100 sentences are false, but the sentence says they are all false. So it doesn’t tell the truth. So if one sentence is true, it is sentence number 99, because 99 sentences are false.

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