On a sheet of paper, you have 100 statements written down.

person 1: At most 0 of the statements are true,

person 2: at most 1 of the statements are true,

person3: at most 2 of the statements are true ... person 100: at most 99 of the statements are true

How many of the statements are true?

Question

Mathematics

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22 February, 22:15

On a sheet of paper, you have 100 statements written down.

person 1: At most 0 of the statements are true,

person 2: at most 1 of the statements are true,

person3: at most 2 of the statements are true ... person 100: at most 99 of the statements are true

How many of the statements are true?

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Answers (1)

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Lorena Sampson · Answer 1

50

Step-by-step explanation:

If the first statement its true (At most 0 of the statements are true), there are not true statements in the paper. So, the first statement its false.

Now, if the first statement its false, this mean there must be at least 1 true statement in the paper.

Now, if the second statement its true (at most 1 of the statements are true) this implies that the third statement its true (if "at most 1" its true, then "as most 2" must be true).

If any statement (besides the first) its true, then all the statement that follows it must be true.

The first non false statement, then, must be the statement made by the person 51: "At most 50 statements are true"

And the 49 statements that follows are true as well.

On a sheet of paper, you have 100 statements written down.person 1: At most 0 of the statements are true,person 2: at most 1 of the statements are true,person3: at most 2 of the statements are true ... person 100: at most 99 of the statements are trueHow many of the statements are true?

On a sheet of paper, you have 100 statements written down.

person 1: At most 0 of the statements are true,

person 2: at most 1 of the statements are true,

person3: at most 2 of the statements are true ... person 100: at most 99 of the statements are true

How many of the statements are true?