In this investigation we will be looking at the investigation of four numbers and generating them to zero. With this we will be using Microsoft excel. The four numbers for the explanation will be any variable. Take for numbers

For the the row that follows these values the goal will be to take the absolute value of the diference of the number in the column above the row minus the number in the column to the right of the current position. For example the entry will look like this:

The goal of this investigation will be to try and maximize the number of rows we can generate. For example take four numbers you like an try it here.

I chose 15, 21, 31, 19 and got:

15 | 21 | 31 | 19 |

6 | 10 | 12 | 4 |

4 | 2 | 8 | 2 |

2 | 6 | 6 | 2 |

4 | 0 | 4 | 0 |

4 | 4 | 4 | 4 |

0 | 0 | 0 | 0 |

If we examine some others a couple of examples can be reached as so:

99 | 55 | 44 | 11 |

44 | 11 | 33 | 88 |

33 | 22 | 55 | 44 |

11 | 33 | 11 | 11 |

22 | 22 | 0 | 0 |

0 | 22 | 0 | 22 |

22 | 22 | 22 | 22 |

0 | 0 | 0 | 0 |

1 | 2 | 3 | 4 |

1 | 1 | 1 | 3 |

0 | 0 | 2 | 2 |

0 | 2 | 0 | 2 |

2 | 2 | 2 | 2 |

0 | 0 | 0 | 0 |

Try some more on your own...here is the set up...Click here

Is there any connections we can make? Have we gotten more than ten rows? If not we need to continue trying.

The two larges I found were:

2500 | 9000 | 20654 | 40981 |

6500 | 11654 | 20327 | 38481 |

5154 | 8673 | 18154 | 31981 |

3519 | 9481 | 13827 | 26827 |

5962 | 4346 | 13000 | 23308 |

1616 | 8654 | 10308 | 17346 |

7038 | 1654 | 7038 | 15730 |

5384 | 5384 | 8692 | 8692 |

0 | 3308 | 0 | 3308 |

3308 | 3308 | 3308 | 3308 |

0 | 0 | 0 | 0 |

AND

27 | 38 | 44 | 7 |

11 | 6 | 37 | 20 |

5 | 31 | 17 | 9 |

26 | 14 | 8 | 4 |

12 | 6 | 4 | 22 |

6 | 2 | 18 | 10 |

4 | 16 | 8 | 4 |

12 | 8 | 4 | 0 |

4 | 4 | 4 | 12 |

0 | 0 | 8 | 8 |

0 | 8 | 0 | 8 |

8 | 8 | 8 | 8 |

0 | 0 | 0 | 0 |

Is there any pattern we can see?

Try this one:

0 | 941 | 2672 | 5856 |

941 | 1731 | 3184 | 5856 |

790 | 1453 | 2672 | 4915 |

663 | 1219 | 2243 | 4125 |

556 | 1024 | 1882 | 3462 |

468 | 858 | 1580 | 2906 |

390 | 722 | 1326 | 2438 |

332 | 604 | 1112 | 2048 |

272 | 508 | 936 | 1716 |

236 | 428 | 780 | 1444 |

192 | 352 | 664 | 1208 |

160 | 312 | 544 | 1016 |

152 | 232 | 472 | 856 |

80 | 240 | 384 | 704 |

160 | 144 | 320 | 624 |

16 | 176 | 304 | 464 |

160 | 128 | 160 | 448 |

32 | 32 | 288 | 288 |

0 | 256 | 0 | 256 |

256 | 256 | 256 | 256 |

0 | 0 | 0 | 0 |

Now is there anything you can judge from there? Try to find a pattern, I have and haven't has luck :)

When you are down and frustrated, try these and see if these help:

1.

0 | 155 | 440 | 964 |

2.

1000 | 2550 | 5400 | 10642 |

3.

1000 | 7000 | 18037 | 38338 |

4.

0 | 10000000 | 28394732 | 62229538 |

5.

1 | 60 | 168 | 367 |

(1-5 were solutions helped by the problem solving web site)