Assignment 12

Four Numbers Subtracted to Zeros?

Making Connections: Solving One Problem for Two Classes

By

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

 

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)

 

 

 


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