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This is one of my favorite tricks.

First, write the number 68 on a piece of paper and seal it in an envelope.

Then tell the students that you are going to have them pick any five numbers from
the following table of 25 numbers, and you are going to predict the sum.

Give the envelope with your prediction to a student to hold.

The only restriction about picking numbers is that once they have picked a number
from a particular row and column, they cannot pick another number from either
that row or that column.

6 | 5 | 7 | 9 | 10 |

13 | 12 | 14 | 16 | 17 |

11 | 10 | 12 | 14 | 15 |

22 | 21 | 23 | 25 | 26 |

9 | 8 | 10 | 12 | 13 |

How does it work?

The restriction above forces the student to choose exactly one number from each row and column.

So, the sum of the five numbers is really the sum of the 10 numbers of the addition table (the blue numbers in the row and column headings below).

The sum of 2 + 1 + 3 + 5 + 6 + 4 + 11 + 9 + 20 + 7 = 68.

+ | 2 | 1 | 3 | 5 | 6 |
---|---|---|---|---|---|

4 | 6 | 5 | 7 | 9 | 10 |

11 | 13 | 12 | 14 | 16 | 17 |

9 | 11 | 10 | 12 | 14 | 15 |

20 | 22 | 21 | 23 | 25 | 26 |

7 | 9 | 8 | 10 | 12 | 13 |