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boboquack
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Alice wrote $8$ positive numbers on the board and Bob claims that:

  • TwoExactly two of them can be divided by $2$ without remainders.
  • ThreeExactly three of them can be divided by $3$ without remainders.
  • FourExactly four of them can be divided by $4$ without remainders.
  • FiveExactly five of them can be divided by $5$ without remainders.
  • SixExactly six of them can be divided by $6$ without remainders.
  • SevenExactly seven of them can be divided by $7$ without remainders.
  • EightExactly eight of them can be divided by $8$ without remainders.

But as you suspected some of these claims were not right.

What is the maximum number of claims that could be right?

Alice wrote $8$ positive numbers on the board and Bob claims that:

  • Two of them can be divided by $2$ without remainders.
  • Three of them can be divided by $3$ without remainders.
  • Four of them can be divided by $4$ without remainders.
  • Five of them can be divided by $5$ without remainders.
  • Six of them can be divided by $6$ without remainders.
  • Seven of them can be divided by $7$ without remainders.
  • Eight of them can be divided by $8$ without remainders.

But as you suspected some of these claims were not right.

What is the maximum number of claims that could be right?

Alice wrote $8$ positive numbers on the board and Bob claims that:

  • Exactly two of them can be divided by $2$ without remainders.
  • Exactly three of them can be divided by $3$ without remainders.
  • Exactly four of them can be divided by $4$ without remainders.
  • Exactly five of them can be divided by $5$ without remainders.
  • Exactly six of them can be divided by $6$ without remainders.
  • Exactly seven of them can be divided by $7$ without remainders.
  • Exactly eight of them can be divided by $8$ without remainders.

But as you suspected some of these claims were not right.

What is the maximum number of claims that could be right?

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Oray
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Find the maximum number of right claims

Alice wrote $8$ positive numbers on the board and Bob claims that:

  • Two of them can be divided by $2$ without remainders.
  • Three of them can be divided by $3$ without remainders.
  • Four of them can be divided by $4$ without remainders.
  • Five of them can be divided by $5$ without remainders.
  • Six of them can be divided by $6$ without remainders.
  • Seven of them can be divided by $7$ without remainders.
  • Eight of them can be divided by $8$ without remainders.

But as you suspected some of these claims were not right.

What is the maximum number of claims that could be right?