(You are NOT allowed to put the cut piece(s) on top of the other.)

.. Answer ..

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Number of cut = n | Additional pieces | Maximum number of pieces |
---|---|---|

0 | 0 | 1 |

1 | +1 | 2 |

2 | +2 | 4 |

3 | +3 | 7 |

4 | +4 | 11 |

5 | +5 | 16 |

6 | +6 | 22 |

7 | +7 | 29 |

8 | +8 | 37 |

9 | +9 | 46 |

10 | +10 | 56 |

Conclusion::

Maximum number of pieces = 1+1(if n>=1)+2(if n>=2)+3(if n>=3)+4(if n>=4)+ ···········

or Maximum number of pieces = ( 2 + n + n² ) / 2