Take the month and day of your birthday and

- Multiply the number of the month by 5
- Add 7
- Multiply by 4
- Add 13
- Multiply by 5
- Add the day of the month
- Subtract 205

So, you have your doubts and go through the calculation to humor the sender. Let's see, my birthday is May 7th, so I should get 507.

- 5 times 7 is 35
- 35 plus 7 is 42
- 42 times 4 is 168
- 168 plus 13 is 181
- 181 times 5 is 905
- 905 plus 7 is 912
- 912 minus 205 is 507

Well, it's actually pretty straightforward and you can easily make up your own math magic tricks once you see how it's done.

Let's first start at the end and think about the resulting number. The last two digits are the day of the month and the first digit or digits are the month number.

- May 7th = 507
- September 20th = 920
- November 12th = 1112
- January 30 = 130

- May 7th = 5 * 100 + 7 = 507
- September 20th = 9 * 100 +20 = 920
- November 12th = 11 * 100 + 12 = 1112
- January 30 = 1 * 100 + 30 = 130

Multiply the number of the month by 5 | 5m |

Add 7 | 5m + 7 |

Multiply by 4 | (5m + 7) * 4 |

Add 13 | (5m + 7) * 4 + 13 |

Multiply by 5 | ((5m + 7) * 4 + 13) * 5 |

Add the day of the month | ((5m + 7) * 4 + 13) * 5 + d |

Subtract 205 | ((5m + 7) * 4 + 13) * 5 + d - 205 |

So, for this trick to work ((5m + 7) * 4 + 13) * 5 + d - 205 must be equal to 100m + d. Let's simplify our equation and see.

((5m + 7) * 4 + 13) * 5 + d - 205 | = | 100m + d |

(20m + 28 + 13) * 5 + d - 205 |
= | 100m + d |

(20m + 41) * 5 + d - 205 |
= | 100m + d |

100m + 205 + d - 205 |
= | 100m + d |

100m + d |
= | 100m + d |

It works! All those 7 steps are really doing is multiplying the month by 100 and adding the day. You can see that it doesn't matter what the values of 'm' and 'd' are, the trick will always work for anyone's birthday.

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## Comments

To much math for me. I see it works but don't get the design part.

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