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# Think of Two Numbers Poster

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### Consecutive Numbers

### Days and Dates

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Age 11 to 14

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- Problem
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I subtract 9 from your answer, and the digits of the number that I'm left with, are your two numbers.

For example, if your final answer is 74, when I subtract 9, I get 65, so I know your numbers were 6 and 5.

**How does it work?**

If the two numbers are $a$ and $b$,

Take one of your numbers |
$a$ |

Add $1$ |
$a+1$ |

Multiply by $5$ |
$5(a+1) = 5a+5$ |

Add $1$ again |
$5a+5+1 = 5a+6$ |

Double your answer |
$2(5a+6) = 10a+12$ |

Subtract $1$ |
$10a+12-1 = 10a+11$ |

Add your second number |
$10a + 11 + b$ |

Add $2$ |
$10a + 11 + b + 2 = 10a + b + 13$ |

Double again |
$2(10a + b + 13) = 20a + 2b + 26$ |

Subtract $8$ |
$20a + 2b + 26 - 9 = 20a + 2b + 18$ |

Halve this number |
$\frac12(20a + 2b + 18) = 10a + b + 9$ |

Final answer is $10a + b + 9$, so I subtract $9$ to leave $10a+b$

$10a + b$ is $a$ tens and $b$ ones

Tens | Ones |

$a$ | $b$ |

Since $a$ and $b$ are both less than $10$, they fit in the tens and ones columns and so they are the digits of the number.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...