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The rec.puzzles Hall of Fame is a compilation of over 500 of the most popular puzzles that have been posted and discussed in the rec.puzzles newsgroup. In most cases a detailed solution has been provided.

Many of these puzzles also appear in Braingle's own collection.

   
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Categories : logic : hundred.p

There is a piece of paper with 100 sentences written on:
"       1. Exactly one sentence on this page is false.
        2. Exactly two sentences on this page are false.
        3. Exactly three sentences on this page are false.
        4. Exactly four sentences on this page are false.
        5. Exactly five sentences on this page are false.
        .
        .
        .
        99. Exactly 99 sentences on this page are false.
        100. Exactly 100 sentences on this page are false."

How many sentences are false and how many are true?
What if we replace "exactly" by "at least"?


Solution

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