# Making Connections: Solving One Problem for Two Classes

## Jen Curro

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

A B C D

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:

|A-B| |B-C| |C-D| |D-A|

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

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)