Some Manual Examples

hamba

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With Acknowledgements to Nix9 and Dommac2000 for all their work.

For a better understanding of how the system works see Nix9's exellent explanations here:

http://www.world-of-digital.com/forums/showthread.php?t=41294

and here:

http://www.world-of-digital.com/forums/showthread.php?t=42394



Ref23: = 131

23: 131
24: 970138462 (5)
25: 8845
26: 536820741 (9)

9701384625 -> 0123456789 ---Apply 1st 1 of ref 23
0123456789 -> 2384697150

S| 2384697150 ---Apply 3 of ref 23
-----------------
8| 8469715023
8| 8469715023
4| 7150238469
5| 9715023846

Apply final 1 of ref 23 --- reading down reorder from left

5368207419 -> 0123456789 ---ref line,read each digit off 1st,2nd,3rd,4th
--------------------------------
8469715023 -> 1274086593 ---1st
8469715023 -> 1274086593 ---2nd
7150238469 -> 3621475859 ---3rd
9715023846 -> 2407891356 ---4th

0612342 - 1234 = 2718
 
Last edited:

hamba

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Ref23: = 223

ref 23: 223
ref 24: 1324
ref 25: 3142
ref 26: 1446


1324 - 1234
1234 - 1324

3142 - 1234
1234 - 2413 reorder by 1324 = 2143

1446 reorder by 2143 = 4164

S| 0123456789
-----------------
4| 6789012345
1| 9012345678
6| 4567890123
4| 6789012345


6705 reorder by 2143 = 7650 = 3596
 

hamba

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Ref23: = 231

23: 231
24: 3214
25: 3439
26: 804675213 (9)

3214 => 1234 --- Apply 2 of ref 23 to ref 24
1234 => 3214

3439 = 3439 --- reordered by 3214

S| 0123456789 --- Apply 3 of ref 23
------------------
3| 7890123456
4| 6789012345
3| 7890123456
9| 1234567890

Apply 1 of ref 23

8046752139 -> 0123456789 ---ref line,read each digit off 1st,2nd,3rd,4th
--------------------------------
7890123456 -> 8435920176
6789012345 -> 7324819065
7890123456 -> 8435920176
1234567890 -> 2879364510

2202400 - 0240* - 4200 = 9282 ---*reorder by 3214
 

hamba

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Ref23: = 233

23: 233
24: 4321
25: 7996
26: 9687

4321 -> 1234 ---Apply 2 of ref23
1234 -> 4321

7996 - 6997 --- reordered by 4321

S| 0123456789 --- Apply 1st 3 of ref23
------------------
6| 4567890123
9| 1234567890
9| 1234567890
7| 3456789012

9687 - 7869 --- reordered by 4321

Apply 2nd 3 of ref23

--------------------0123456789
----------------------------------
4567890123 S7 7890123456
1234567890 S8 3456789012
1234567890 S6 5678901234
3456789012 S9 4567890123

3678509 - 7850* - 0587 = 7831 -------*reorder by 4321
 

hamba

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Ref23: = 312

23: 312
24: 6582
25: 697435218 (0)
26: 4123

S| 0123456789 ---Apply 3 of ref 23
-----------------
6| 4567890123
5| 5678901234
8| 2345678901
2| 8901234567

Apply 1 of ref 23 --- reading down reorder from left

6974352180 -> 0123456789 ---ref line,read each digit off 1st,2nd,3rd,4th
--------------------------------
4567890123 -> 3108794625 ---1st
5678901234 -> 4219805736 ---2nd
2345678901 -> 1986572402 ---3rd
8901234567 -> 7542138069 ---4th

4123 -> 1234 ---Apply 2 of ref 23
1234 -> 2341

0209674 - 0967* - 9670 = 5547 ---* reorder by 2341
 

hamba

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Ref23: = 313

23 313
24 7937
25 340865127
26 5405

* 0123456789
---------------
7 3456789012
9 1234567890
3 7890123456
7 3456789012

3408651279 > 0123456789
-------------------------------
3456789012 > 5903487162
1234567890 > 3781265940
7890123456 > 9347821506
3456789012 > 5903487162

5903487162 >5> 8716259034
3781265940 >4> 5940378126
9347821506 >0> 9347821506
5903487162 >5> 8716259034

0123456789
--------------
8716259034
5940378126
9347821506
8716259034

2234135 = 6336
 

hamba

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Ref23: = 321

23 321
24 6038
25 4321
26 931065728

* 0123456789
-----------------
6 4567890123
0 0123456789
3 7890123456
8 2345678901

1234
4321 = 4321

9310657284 -> 0123456789
--------------------------------
4567890123 -> 7615398024
0123456789 -> 3271954680
7890123456 -> 0948621357
2345678901 -> 5493176802

4063632 - 6363 =3636 = 5486
 

hamba

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Ref23: = 323

23: 323
24: 5278
25: 3142
26: 7204

* 0123456789
----------------
5 5678901234
2 8901234567
7 3456789012
8 2345678901

1234 > 2413*
3142 > 1234

7204 = 2470

-----------------0123456789
-------------------------------
5678901234 2 3456789012
8901234567 4 4567890123
3456789012 7 6789012345
2345678901 0 2345678901

3170494 = 7049 = 0974 = 3336
 

hamba

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Ref23: = 1211

23: 1211
24: 597318624(0)
25: 4231
26: 872690453(1)
27: 182945607(3)

5973186240 -> 0123456789 ---Apply 1st 1 of ref 23
0123456789 -> 9473806251

4231 => 1234 ---Apply 2 of ref 23
1234 => 4231

8726904531 -> 0123456789 ---Apply 2nd 1 of ref 23
9473806251 -> 0175623498

Apply 3rd 1 of ref 23

1829456073 -> 0123456789---ref line
--------------------------------
0175623498 -> 4078623915

1092271 - 9227* - 7229 = 9775 ---* reorder by 4231
 

hamba

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Ref23: = 1212

23: 1212
24: 345610897 ( 2)
25: 4123
26: 176593204 (8)
27: 1243

3456108972 -> 0123456789 ---Apply 1st 1 of ref 23
0123456789 -> 5490123867

4123 => 1234 ---Apply 1st 2 of ref 23
1234 => 2341

1765932048 -> 0123456789 ---Apply 2nd 1 of ref 23
5490123867 -> 8532609471

1243 => 1234 ---Apply 2nd 2 of ref 23
1234 => 1243

0123456789 ---ref line
--------------
8532609471 ---read all four digits off this line

2224354 - 2435* - 2453** - 4532 = 6023 ---*reorder by 1243; **reorder by 2341
 

hamba

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Ref23: = 1213

23: 1213
24: 379241508 (6)
25: 3214
26: 371659042 (8)
27: 2266

3792415086 -> 0123456789 --- Apply 1st 1 of ref23
0123456789 -> 7530469182

3214 -> 1234 ---Apply 2 of ref23
1234 -> 3214

3716590428 -> 0123456789 --- Apply 2nd 1 of ref23
7530469182 -> 9387140526

2266 - 6226 --- reordered by 3214

S| 9387140526 --- Apply 3 of ref23
-----------------
6| 1405269387
2| 2693871405
2| 2693871405
6| 1405269387

0123456789 ---ref line, read each digit off 1st,2nd,3rd,4th
--------------
1405269387 ---1st
2693871405 ---2nd
2693871405 ---3rd
1405269387 ---4th

4052413 - 5241* - 4251 = 2974 ---*reorder by 3214
 

hamba

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Ref23: = 1231

23: 1231
24: 420581693
25: 2134
26: 8126
27: 471685209

0123456789 => 2518036947
4205816937 => 0123456789

2134 => 1234
1234 => 2134

8126 rearranges to 1826

-------------------4716852093
---------------------------------
2518036947 1 7251803694
2518036947 8 1803694725
2518036947 2 4725180369
2518036947 6 0369472518

0456421 - 5642 - 6542 = 1942
 

hamba

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Ref23: = 1232

23: 1232
24: 126548307
25: 4132
26: 6948
27: 1234

1265483079 -> 0123456789 --- (Apply 1)
0123456789 -> 7016432859

4132 => 1234 ---(Apply 2)
1234 => 2431 ----------------(6948 -> 9846)

S| 7016432859 ---(Apply 3)
------------------
9| 0164328597
8| 1643285970
4| 2859701643
6| 4328597016

1234 => 1234 ---(Apply 4)
1234 => 1234

0123456789 ---ref line, read each digit off 1st,2nd,3rd,4th
--------------
0164328597 ---1st
1643285970 ---2nd
2859701643 ---3rd
4328597016 ---4th

2312340 - 1234* - 1234 - 2431 = 6293 *---(Apply result of 4 then 2)
 

hamba

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Ref23: = 1233

23: 1233
24: 197836254
25: 1324
26: 6088
27: 5177

1978362540 -> 0123456789 ---Apply 1 of ref23
0123456789 -> 9064875231

1324 -> 1234 ---Apply 2 of ref23
1234 -> 1324

6088 - 6808 --- reordered by 1324

S| 9064875231 --- Apply 1st 3 of ref23
-----------------
6| 8752319064
8| 6487523190
0| 9064875231
8| 6487523190

5177 - 5717 --- reordered by 1324

Apply 2nd 3 of ref23

-------------------0123456789 ---ref line, read each digit off 1st,2nd,3rd,4th
---------------------------------
8752319064-S5-1906485723 ---1st
6487523190-S7-7523190648 ---2nd
9064875231-S1-1906487523 ---3rd
6487523190-S7-7523190648 ---4th

4036586 - 3658* - 3568 = 6974 --- reorder by 1324
 

hamba

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Ref23: = 2113

23: 2113
24: 4321
25: 702563418 (9)
26: 570398241 (6)
27: 9288



4321 -> 1234 ---Apply 2 of ref23
1234 -> 4321

7025634189 -> 0123456789 --- Apply 1st 1 of ref23
0123456789 -> 1725634089

5703982416 -> 0123456789 --- Apply 2nd 1 of ref23
1725634089 -> 2845019736

9288 - 8829 --- reordered by 4321

S| 2845019736 --- Apply 3 of ref23
------------------
8| 4501973628
8| 4501973628
2| 3628450197
9| 8450197362


0123456789 ---ref line, read each digit off 1st,2nd,3rd,4th
--------------
4501973628 ---1st
4501973628 ---2nd
3628450197 ---3rd
8450197362 ---4th

2512346 - 1234* - 4321 = 9124 ---*reorder by 4321
 
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