PUZZLE #3 (from the 9th to the 24th of February 2010)

A WICKED FRIEND

James asked Sharon what her telephone number was. Sharon, who is very fond of Mathematics, answered this:“It is the only 9-digit number whose digits are all different and different from zero and in which ANY two consecutive digits make a number which is divisible either by 7 or by 13.

Well, what’s Sharon ’s telephone number?

SOLUTION

We've received 5 correct solutions from:

Zsofia Zentai (Hungary)

Reka Vass (Hungary)

Máté Fenyvesi (Hungary)

Kristynna Mandá ková ( Czech Republic)

Joan Josep Pla (Spain)

Luisa Wiechert (Germany)

Julian Kaping (Germany).

Here, we plublish Zsofia Zentia's solution

SOLUTION

We've received 5 correct solutions from:

Zsofia Zentai (Hungary)

Reka Vass (Hungary)

Máté Fenyvesi (Hungary)

Kristynna Mandá ková ( Czech Republic)

Joan Josep Pla (Spain)

Luisa Wiechert (Germany)

Julian Kaping (Germany).

Here, we plublish Zsofia Zentia's solution

At first, we need to find all those 2-digit numbers that are divisible by 7 or 13.

ð Numbers that are divisible by 7:

o 14, 21, 28, 35, 42, 49, 56, 63, ~~70~~, ~~77~~, 84, 91 and 98.

ð Numbers that are divisible by 13:

o 13, 26, 39, 52, 65, 78 and 91.

After a little observation we find that:

ð Neither of these numbers ends by 7à the telephone number may start with 78

ð Only number 4 can follow number 8. à784

Two numbers can follow 4: number 2 or 9.

3 ^{rd} number of the phone number | 4th | 5th | 6th | 7th | 8th | 9th |

4 | 2 | 8 | ||||

4 | 2 | 1 | 4 | |||

4 | 2 | 1 | 3 | 5 | 6 | 3 |

4 | 2 | 1 | 3 | 5 | 6 | 5 |

4 | 2 | 1 | 3 | 5 | 2 | |

4 | 2 | 1 | 3 | 9 | 8 | |

4 | 2 | 1 | 3 | 9 | 1 | |

4 | 2 | 6 | 3 | 5 | 6 | |

4 | 2 | 6 | 3 | 5 | 2 | |

4 | 2 | 6 | 3 | 9 | 1 | 4 |

4 | 2 | 6 | 3 | 9 | 1 | 3 |

4 | 2 | 6 | 3 | 9 | 8 | |

4 | 2 | 6 | 5 | 6 | ||

4 | 2 | 6 | 5 | 2 | ||

4 | 9 | 8 | ||||

4 | 9 | 1 | 4 | |||

4 | 9 | 1 | 3 | 9 | ||

4 | 9 | 1 | 3 | 5 | 6 | 3 |

4 | 9 | 1 | 3 | 5 | 6 | 5 |

4 | 9 | 1 | 3 | 5 | 2 | 1 |

4 | 9 | 1 | 3 | 5 | 2 | 8 |

4 | 9 | 1 | 3 | 5 | 2 | 6 |

So Sharon ’s phone number is:

__784913526.__
以簡單的行為愉悅他人的心靈，勝過千人低頭禱告........................................

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