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# The Pick 3 Benford Matrix

Topic closed. 22 replies. Last post 10 years ago by WSN1.

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Findlay, Ohio
United States
Member #4855
May 28, 2004
400 Posts
Offline
 Posted: January 6, 2007, 10:03 pm - IP Logged

In my recent post http://www.lotterypost.com/thread/148025 , I illustrated how Benford's Law can be shown to apply to the skips found within any Pick 3 game.  The graphs shown within that post reference each of the listed states game from a historical perspective...meaning that the entire draw history of each state was used to gather the skip data.

However, the entire draw history does not necessarily have to be used in order to observe the "Law."  You can take any states game, that has a good history behind it, and by examining the last 1,000 draws aquire very similar results.  Simply put, by looking at how far out (in consecutive games) that each of the last 1,000 numbers drawn was at the time of its last hit, you can see Benford's Law in action.

For example, if you look at the last 1,000 games in Ohio and for each straight that was drawn determine the skip interval of that specific hit to its previous hit, you can observe how the game closely follows the Law .

Graphing out the skips for each of the straights that fell in Ohio for the last 1,000 games produces the following graph:

Of course this same pattern should emerge for any Pick 3 game in any given state.  Here is Georgia as a second example:

The reason that the skips will so closely follow this pattern is that because at any givin point in time, there will be very close to 1/3 of the 1,000 possible Pick 3 straights capable of ending their skip at a value that is in accordance to Benford's Law!

THE BENFORD MATRIX

I dubbed this special group of 1/3 the "Benford Matrix" since it encompasses all of the straighs whos skips are out at a value that starts with the leading digit of one.  The skip ranges for these straights include the following:

1 (last straight drawn)
10 through 19 games ago
100 through 199 games ago
1,000 through 1,999 games ago

I call any and all straights that have not been drawn for an amount of consecutive games that fall within any of these specified ranges the "Benford Numbers."  The numbers that make up this group or matrix are unlike any other.  In grouping numbers to be tracked, the most common approach is to group the numbers based on the digits they contain as well as their high/low and even/odd value, their sum or root sum value and also sometimes their frequencies.

The Benford Matrix is quite a bit different.  These numbers are added to the group based on how long its been since they each hit.  The group is not static either: it slightly changes each draw, but over the course of time, the numbers it contains changes dramatically.  I have heard it said (don't remember exactly where) that constantly changing the numbers that you play leads to more wins than playing the same numbers repeatedly.  Judging by the performance of the Benford Matrix this might possibly be true.

The Benford Matrix contains an excellent mixture of numbers.  As I stated before, there are about 333 numbers in this group at any given time.  Around 230 of this amount are the straights that are out between 1000 and 1999 games.  These are the "due" to "over-due" collection of numbers within the group.  Normally, there are also around 85 numbers in this 1/3 that just hit between 100 to 199 games ago.  These 85 numbers, in conjuction with the 9 or 10 that just hit between 10 to 19 games ago...as well as the last combo to be drawn one game ago, comprise the numbers that are set to have short skips or repeats.  So, the Benford Matrix is made from a mixture of both recently drawn and long-out numbers.

Think of randomness as the controlling mechanism, or engine, of the game.  The exhaust created by the engine directly fuels this group of numbers...its like a turbo charged lottery lol.  The same randomness that creates the daily results is the very same randomness that is creating the Benford group of numbers!

I did some testing in Ohio to see how the group would hit over the course of time.  Instead of testing it for an exact 100 or even 1,000 consecutive games, I did something a little different.  I tested it over several median spans.  A median span is a 693 consecutive game span of time, which is the amount of time (games) it takes to have a 50% chance for any straight to be drawn, this also means that 500 unique straights are drawn in this time.  Now, since the group is usually around 333 numbers in size, I expected it to win about about 1/3 of all games...and it did.  For 693 games, 1/3 equates to about 231 hits.  The actual probability for hits from the benford group sum up to be a little over 32% rather than 33.3% or 1/3, so the more precise figure of .32*693=225.77 should be used.

Starting with the last number drawn, I looked back 693 games to see how many hits were from the Benford group.  I recorded this number and also how many of them were unique (I wanted to see how many DIFFERENT numbers were hitting from the group, not just how often the group actually hit).  Once i did this test (starting with the most recent game) I repeated the same test starting with the second to last game, again examining 693 games backwards.  After recording the results, I performed the test a third time...starting with the third most recent game and then a fourth time with the fourth most recent game as so on.  In the end, I had tested 7,971 seperate (but connected by overlap) spans of 693 games.

The Benford group hit an average (and a very tight one at that) of 227.49 times within every 693 consecutive game span.  That equates to 32.82%, which is right on the money for the probabilities involved.  Now for the interesting part.  The amount of unique combos that hit from the group in each span was a very tight average of 205.44.  This shows the the amount of different numbers hitting from the group is extremely high as a percentage (62%).  If you take any static (unchanging) group of numbers and watch their performance over a 693 game span, only about 50% of them should hit.  The unique hits from the Benford Matrix hit at a much higher rate because the numbers played are constantly changing.

To me, perhaps the most interesting aspect of all this is the ratio of unique hits to the size of the matrix they come from.

205.44 * 1.618 (Phi) = 332.401

It could be something, or it could be nothing. More to follow...

~Probability=Odds in Motion~

Findlay, Ohio
United States
Member #4855
May 28, 2004
400 Posts
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 Posted: January 14, 2007, 3:10 pm - IP Logged

Using the Benford Matrix

As I stated above, there are usually about 333 straight numbers in the Benford Matrix at any given time.  These numbers are the ones that are actually capable of hitting (ending their skips) at value that starts with the digit one.  At this moment, there are 341 straights in this matrix for Ohio.

Here is Ohio's current matrix.  The combos are listed in ascending order...the number to the right of each is how many consecutive games ago it was last drawn:

003 1881
007 1197
010 1260
014 1
016 1491
021 1100
029 1019
030 1841
031 1255
033 1367
035 1701
036 129
040 1603
043 156
044 1203
045 1269
050 1642
054 1480
058 146
063 1095
066 1858
067 1145
068 1421
069 1488
071 14
073 1654
079 1107
083 1770
085 184
086 1854
087 18
093 1679
095 128
097 124
098 188
112 126
114 1680
115 165
121 1781
122 1051
124 134
127 1330
128 114
133 1327
134 1018
136 1396
137 1589
140 1484
142 1173
147 1121
148 192
150 193
151 1533
152 1122
158 131
159 1884
160 1674
161 121
162 1374
163 1522
166 1006
167 10
168 176
171 1773
172 1161
183 1638
184 1103
185 172
187 153
188 1890
190 1768
198 196
202 174
203 1067
204 1409
206 1206
209 1749
215 1030
218 1154
220 154
222 187
225 1785
226 182
229 1400
234 1291
240 162
241 1451
242 147
243 104
245 1065
246 166
251 1202
255 157
256 127
262 1270
263 1842
266 1414
269 119
272 1261
275 111
287 1473
290 1544
293 1187
298 132
299 112
303 199
304 1632
306 1134
307 1800
308 1071
310 150
312 148
318 160
322 1209
326 125
327 1564
341 123
345 100
346 1143
348 107
350 1905
352 1137
353 1196
354 1323
355 1956
356 13
357 12
359 1218
360 1977
365 139
368 1417
373 1149
384 1123
385 144
386 1129
395 1510
399 1441
400 1835
401 1346
405 1128
409 1971
413 152
416 1147
418 195
426 1332
427 1022
429 135
430 1265
431 1142
434 1459
437 1233
440 1896
444 1796
452 1732
453 1056
463 1521
465 1556
466 1810
469 1353
471 1523
473 1388
480 1184
482 1224
485 1015
486 171
487 1035
496 1188
498 1046
501 1659
503 117
504 1124
508 136
510 1803
514 1894
519 1974
523 1980
535 1982
538 1369
540 1201
542 181
547 1595
549 1126
552 1519
557 173
558 167
559 1540
560 1288
563 159
564 1104
566 1189
569 1164
574 163
579 1136
581 1821
584 168
585 1033
586 1517
588 1784
593 1171
599 1053
603 185
610 108
611 1767
613 16
614 1231
616 1208
617 1601
620 1455
627 1437
635 1875
640 1917
643 1317
648 1326
650 1010
651 1257
652 1947
655 1735
657 1629
659 113
663 1014
669 1913
670 155
671 1148
674 1739
675 1991
676 1222
680 1563
681 1844
684 198
686 1650
687 120
688 1906
689 1098
690 1713
691 1582
693 1341
697 1042
699 151
704 141
706 1462
707 1392
711 1561
713 1168
719 1320
722 102
723 1082
726 1254
728 1376
729 1805
730 1368
735 1496
738 19
739 1084
740 1418
742 1728
745 1366
748 161
749 115
751 189
752 1099
755 1813
757 1511
762 1763
763 1619
767 1761
768 1442
771 1820
772 1520
782 197
783 179
784 15
785 183
788 1279
790 1088
793 1920
794 1505
803 1816
804 1050
805 1364
806 1958
808 142
810 1016
812 1043
813 1335
815 1319
818 1340
819 1425
820 169
822 164
824 1431
831 1304
832 1213
835 1365
839 191
842 1380
844 1039
846 1446
847 1352
848 1482
856 103
858 118
859 1487
861 1294
863 1626
866 186
867 1339
870 1493
874 1034
879 11
893 1453
895 1979
898 1159
902 158
907 1937
910 1021
912 143
916 1186
917 105
918 1653
919 1325
921 1836
926 1756
931 1791
941 1412
944 17
947 1946
949 1336
954 130
956 1961
958 178
960 1087
963 1502
964 1710
968 1259
972 122
974 1250
978 1865
979 1193
980 145
983 116
991 1955

Here are some facts to keep in mind while anticipating numbers from the matrix to hit:

• When you see a Benford Number hit, there IS about a 55% chance that another hit from the matrix will occur within the next 2 games.
• When a Benford Number hits, there is about a 70% chance that another hit from the matrix will occur within the next 3 games!
• 90% of all Benford hits occur within 6 games of their last hit.

These percentages are based on probability and should apply to the specific matrices of each state.  The statistical performance of the probabilites are right on par in Ohio.

In Ohio, the last four consecutive games have not consisted of numbers from the Benford Group, so watch for one to hit here very soon.  When the next Benford Number actually does hit, I would anticipate another hit within the next two games afterwards because that 55% chance/event is extremely due!

341 numbers is way too many to play.  The idea is to use the group as a pool to choose numbers from.  Since digits, root sum and other such measurements should more or less be equally distributed across the matrix, it will help to use other indicators while choosing.  For example, in position-two (Ohio), the digit 2 has not been drawn for 59 games now.  Banking on a Benford Number with a middle digit 2 will lead you to these 31 numbers from the matrix above:

021
029
121
122
124
127
128
220
222
225
226
229
322
326
327
426
427
429
523
620
627
722
723
726
728
729
820
822
824
921
926

Of course you can always filter for boxed and doubles as well.

~Probability=Odds in Motion~

Blundering Time Traveler

United States
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December 25, 2005
1540 Posts
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 Posted: January 16, 2007, 3:02 pm - IP Logged

Always enjoy your posts Thoth, and the work that goes into them. This one is no exception - very instructive and confirms much.... Thank you.

"In the Beginning was the Point". According to Lottery Lore, these are the only words written in the long-lost ancient Pick 3 Codex - The Scroll of Harmony .Those who came later, The Lottery LoreKeepers, intuited the rest of the riddle as they charted the Point's evolution through TIME by connecting its periods and exposing relationships that predict the next draw(7th): "The Point(1st draw) was born, began to grow and in its bold adolescence became the line(2nd draw), knew young adulthood in the triangle(3rd draw), stable maturity by the square(4th draw), older age as the pentagon(5th draw), and embraced 'death' in the hexagon(6th draw). Here lies the CIrcle of a lottery draw's life and it is Immutable; For as the Point seeds, flowers and fruits, it is changed but essentially unchanged, as it forever rises in ReBirth(7th draw)"

Illinois
United States
Member #46704
September 23, 2006
3692 Posts
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 Posted: January 16, 2007, 3:23 pm - IP Logged

Toth this is some deep stuff,  what interests me the most

is the fact that you are targeting str8's

Keep up the good work

Men Lie Women Lie Numbers Dont

The Carolinas - Charlotte
United States
Member #21627
September 12, 2005
4138 Posts
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 Posted: January 16, 2007, 3:25 pm - IP Logged

Straights seem to be the way to go. I love this post...

The North Carolina Education Lottery - so much a joke that here are their mascots:

The Carolinas - Charlotte
United States
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September 12, 2005
4138 Posts
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 Posted: January 16, 2007, 3:27 pm - IP Logged

I would be inclined to wait for a skip of 2 to 3 of a Benford number and then move in for the winner. Progressively, this could be done easily.

Thoth - do you have Ohio's max skip of a Benford number? How easy is this to apply to other states/draws?

The North Carolina Education Lottery - so much a joke that here are their mascots:

ORLANDO, FLORIDA
United States
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June 3, 2004
6065 Posts
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 Posted: January 16, 2007, 6:44 pm - IP Logged

Using the Benford Matrix

As I stated above, there are usually about 333 straight numbers in the Benford Matrix at any given time.  These numbers are the ones that are actually capable of hitting (ending their skips) at value that starts with the digit one.  At this moment, there are 341 straights in this matrix for Ohio.

Here is Ohio's current matrix.  The combos are listed in ascending order...the number to the right of each is how many consecutive games ago it was last drawn:

003 1881
007 1197
010 1260
014 1
016 1491
021 1100
029 1019
030 1841
031 1255
033 1367
035 1701
036 129
040 1603
043 156
044 1203
045 1269
050 1642
054 1480
058 146
063 1095
066 1858
067 1145
068 1421
069 1488
071 14
073 1654
079 1107
083 1770
085 184
086 1854
087 18
093 1679
095 128
097 124
098 188
112 126
114 1680
115 165
121 1781
122 1051
124 134
127 1330
128 114
133 1327
134 1018
136 1396
137 1589
140 1484
142 1173
147 1121
148 192
150 193
151 1533
152 1122
158 131
159 1884
160 1674
161 121
162 1374
163 1522
166 1006
167 10
168 176
171 1773
172 1161
183 1638
184 1103
185 172
187 153
188 1890
190 1768
198 196
202 174
203 1067
204 1409
206 1206
209 1749
215 1030
218 1154
220 154
222 187
225 1785
226 182
229 1400
234 1291
240 162
241 1451
242 147
243 104
245 1065
246 166
251 1202
255 157
256 127
262 1270
263 1842
266 1414
269 119
272 1261
275 111
287 1473
290 1544
293 1187
298 132
299 112
303 199
304 1632
306 1134
307 1800
308 1071
310 150
312 148
318 160
322 1209
326 125
327 1564
341 123
345 100
346 1143
348 107
350 1905
352 1137
353 1196
354 1323
355 1956
356 13
357 12
359 1218
360 1977
365 139
368 1417
373 1149
384 1123
385 144
386 1129
395 1510
399 1441
400 1835
401 1346
405 1128
409 1971
413 152
416 1147
418 195
426 1332
427 1022
429 135
430 1265
431 1142
434 1459
437 1233
440 1896
444 1796
452 1732
453 1056
463 1521
465 1556
466 1810
469 1353
471 1523
473 1388
480 1184
482 1224
485 1015
486 171
487 1035
496 1188
498 1046
501 1659
503 117
504 1124
508 136
510 1803
514 1894
519 1974
523 1980
535 1982
538 1369
540 1201
542 181
547 1595
549 1126
552 1519
557 173
558 167
559 1540
560 1288
563 159
564 1104
566 1189
569 1164
574 163
579 1136
581 1821
584 168
585 1033
586 1517
588 1784
593 1171
599 1053
603 185
610 108
611 1767
613 16
614 1231
616 1208
617 1601
620 1455
627 1437
635 1875
640 1917
643 1317
648 1326
650 1010
651 1257
652 1947
655 1735
657 1629
659 113
663 1014
669 1913
670 155
671 1148
674 1739
675 1991
676 1222
680 1563
681 1844
684 198
686 1650
687 120
688 1906
689 1098
690 1713
691 1582
693 1341
697 1042
699 151
704 141
706 1462
707 1392
711 1561
713 1168
719 1320
722 102
723 1082
726 1254
728 1376
729 1805
730 1368
735 1496
738 19
739 1084
740 1418
742 1728
745 1366
748 161
749 115
751 189
752 1099
755 1813
757 1511
762 1763
763 1619
767 1761
768 1442
771 1820
772 1520
782 197
783 179
784 15
785 183
788 1279
790 1088
793 1920
794 1505
803 1816
804 1050
805 1364
806 1958
808 142
810 1016
812 1043
813 1335
815 1319
818 1340
819 1425
820 169
822 164
824 1431
831 1304
832 1213
835 1365
839 191
842 1380
844 1039
846 1446
847 1352
848 1482
856 103
858 118
859 1487
861 1294
863 1626
866 186
867 1339
870 1493
874 1034
879 11
893 1453
895 1979
898 1159
902 158
907 1937
910 1021
912 143
916 1186
917 105
918 1653
919 1325
921 1836
926 1756
931 1791
941 1412
944 17
947 1946
949 1336
954 130
956 1961
958 178
960 1087
963 1502
964 1710
968 1259
972 122
974 1250
978 1865
979 1193
980 145
983 116
991 1955

Here are some facts to keep in mind while anticipating numbers from the matrix to hit:

• When you see a Benford Number hit, there IS about a 55% chance that another hit from the matrix will occur within the next 2 games.
• When a Benford Number hits, there is about a 70% chance that another hit from the matrix will occur within the next 3 games!
• 90% of all Benford hits occur within 6 games of their last hit.

These percentages are based on probability and should apply to the specific matrices of each state.  The statistical performance of the probabilites are right on par in Ohio.

In Ohio, the last four consecutive games have not consisted of numbers from the Benford Group, so watch for one to hit here very soon.  When the next Benford Number actually does hit, I would anticipate another hit within the next two games afterwards because that 55% chance/event is extremely due!

341 numbers is way too many to play.  The idea is to use the group as a pool to choose numbers from.  Since digits, root sum and other such measurements should more or less be equally distributed across the matrix, it will help to use other indicators while choosing.  For example, in position-two (Ohio), the digit 2 has not been drawn for 59 games now.  Banking on a Benford Number with a middle digit 2 will lead you to these 31 numbers from the matrix above:

021
029
121
122
124
127
128
220
222
225
226
229
322
326
327
426
427
429
523
620
627
722
723
726
728
729
820
822
824
921
926

Of course you can always filter for boxed and doubles as well.

Thoth,

1/15/07 Mid 614

1/16/07 Mid 675

This is very interesting, Thoth like always.

Thanks

Stone Mountain*Georgia
United States
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November 2, 2002
10491 Posts
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 Posted: January 16, 2007, 8:17 pm - IP Logged

Mother Nature ... She's a real character sometimes. LOL Just a little too cute for me...

 Tue, Jan 16, 2007 6-7-5 2-3-2 3-7-1-5 7-1-0-2

The only real failure .....is the failure to try.

Luck is a very rare thing....... Odds not so much.

Odds never change .....but probability does.

Win d

Findlay, Ohio
United States
Member #4855
May 28, 2004
400 Posts
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 Posted: January 22, 2007, 12:03 pm - IP Logged

I would be inclined to wait for a skip of 2 to 3 of a Benford number and then move in for the winner. Progressively, this could be done easily.

Thoth - do you have Ohio's max skip of a Benford number? How easy is this to apply to other states/draws?

CPS10,

Sorry for the delayed response...

The max skip in Ohio for the Benford group is 20 draws.  Here is the top 30 largest skips of the group:

 Top 30 Skips 1 20 2 20 3 19 4 18 5 17 6 17 7 17 8 16 9 16 10 16 11 15 12 15 13 15 14 14 15 14 16 14 17 14 18 14 19 14 20 13 21 13 22 13 23 13 24 13 25 12 26 12 27 12 28 12 29 12 30 12

This table represents the largest skips of the benford group when examining the draw history from game 2,000 through 10,781.  If you start the test at game #1 you will have some much larger skips for the group (Top 3 are: 76, 48, 47).  I don't count these because it takes about 2000 draws to start to establish the stratetgy to begin with.

~Probability=Odds in Motion~

Anywhere & Everywhere
United States
Member #10713
January 23, 2005
290 Posts
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 Posted: February 3, 2007, 7:43 pm - IP Logged

Thoth,

Tell me what do you think the significance may be from this test. I just recorded a group of 1,000 recent draws in TX with how many had a sum of 10-19, using the benford group first digit #1, the result was the infamous 666 times. Hmmmm!

Also, I understand I am applying a slightly different perspective for review. However, if I am understanding correctly with your application, you are changing the combos every draw accordingly to various #1 digit skip groups?

Also, more food for thought. There has been a lot of studies done on end digits analysis, like end digit, last digit, short sum, root, etc...I wonder if they can be combined at some point, once this part has been ironed out definitively.

Anywhere & Everywhere
United States
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January 23, 2005
290 Posts
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 Posted: February 3, 2007, 10:41 pm - IP Logged

Well, I dont want to take this study too far ofcourse, however, I think there is a relationship. One reason why there was 66.6% hit rate with sums 10-19, is that there are more combos in this range than 0-9 and 20-27 range. Although, I have no mathematical factual basics, I believe that the end digits 0-5 are most likely. Therefore, Im thinking skips 11-15 are more likely than skips 16-19. Well probably because of something you said before. If something has been out 2-9 draws, then the further out each draw the greater the probability of occurrence. Over the same period sums 11-15 hit 354x and sums 16-19 hit 241x

Anywhere & Everywhere
United States
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January 23, 2005
290 Posts
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 Posted: February 3, 2007, 10:59 pm - IP Logged

Can we make this assumption that 40% of draws will come from the following 6 out of the 27 sums > 10-15?

Greenwich, CT
United States
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May 24, 2004
1822 Posts
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 Posted: February 5, 2007, 9:53 am - IP Logged

You could also apply the 'probability of probability' to guessing when to play the Benford 1's, the 2's, the 3's etc., adding another layer.

I think that lottery analysis is like slicing a grapefruit.  For Pick 3, imagine dividing the grapefruit into one thousand equal pieces.  Think of cutting it down the middle, you will have two equal parts, and you can place a bet on which one is more likely to occur.  Then slice horizontally, so you have quadrants.  Each filter that you apply provides a slice at a different angle, eventually you're left with a very small piece of grapefruit, hopefully the winning number!  Benford's Law can provide a couple of excellent cuts through that grapefruit.

Findlay, Ohio
United States
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May 28, 2004
400 Posts
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 Posted: February 5, 2007, 9:34 pm - IP Logged

You could also apply the 'probability of probability' to guessing when to play the Benford 1's, the 2's, the 3's etc., adding another layer.

I think that lottery analysis is like slicing a grapefruit.  For Pick 3, imagine dividing the grapefruit into one thousand equal pieces.  Think of cutting it down the middle, you will have two equal parts, and you can place a bet on which one is more likely to occur.  Then slice horizontally, so you have quadrants.  Each filter that you apply provides a slice at a different angle, eventually you're left with a very small piece of grapefruit, hopefully the winning number!  Benford's Law can provide a couple of excellent cuts through that grapefruit.

I like waiting for one of the "Benford numbers" to hit...then gamble on the 55% chance that another one will hit within the next two games.  Of course other factors have to be included to narrow the picks in that group down

~Probability=Odds in Motion~

Wyncote,Pa
United States
Member #3206
January 3, 2004
62357 Posts
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 Posted: February 7, 2007, 12:06 am - IP Logged

Over the same period sums 11-15 hit 354x and sums 16-19 hit 241x

Using sums is a very effective way to win in the pick3. The most common group of sums are the 12-15 group. To arrive at a sum just add all three digits together. If you take away doubles you have  only 10 numbers to work in each of these 4 groups. In the month of Jan. for NY there were 16 hits from the 12-15 group. Not bad considering there only 40 possible non-match numbers from these sums. Go back the past couple weeks in your state and look for the hottest sum and most due sum from the 12-15 group, and play the numbers in it. For example in NY the sum 13 is the most due to show, while the 15 has been the hottest this year. Each time a number hits in the 12-15 group mark it down, this way you can see whats hot, and overdue. Here is a list of the 12-15 sums, minus the doubles.

12-039-048-057-156-147-237-246-345-129-138

13-049-058-067-139-148-157-238-247-256-346

14-059-068-149-158-167-239-248-257-347-356

15-069-078-159-168-249-258-267-348-357-456

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 12 15 6.8% 039 048 057 066 129 138 147 156 228 237 246 255 336 345 444 13 15 6.8% 049 058 067 139 148 157 166 229 238 247 256 337 346 355 445 14 15 6.8% 059 068 077 149 158 167 239 248 257 266 338 347 356 446 455 15 15 6.8% 069 078 159 168 177 249 258 267 339 348 357 366 447 456 555

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000 001 002 003 004 005 006 007 008 009 011 012 013 014 015 016 017 018 019 022 023 024 025 026 027 028 029 033 034 035 036 037 038 039 044 045 046 047 048 049 055 056 057 058 059 066 067 068 069 077 078 079 088 089 099 111 112 113 114 115 116 117 118 119 122 123 124 125 126 127 128 129 133 134 135 136 137 138 139 144 145 146 147 148 149 155 156 157 158 159 166 167 168 169 177 178 179 188 189 199 222 223 224 225 226 227 228 229 233 234 235 236 237 238 239 244 245 246 247 248 249 255 256 257 258 259 266 267 268 269 277 278 279 288 289 299 333 334 335 336 337 338 339 344 345 346 347 348 349 355 356 357 358 359 366 367 368 369 377 378 379 388 389 399 444 445 446 447 448 449 455 456 457 458 459 466 467 468 469 477 478 479 488 489 499 555 556 557 558 559 566 567 568 569 577 578 579 588 589 599 666 667 668 669 677 678 679 688 689 699 777 778 779 788 789 799 888 889 899 999

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