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Command-based Reduction System for PICK 4 games

FILTER FUNCTIONS II
The most important part of the reduction is the use of filters. For simplicity reasons we show the filter selections as SELECT picking only numbers that fit the selection. Every command is also available as UNSELECT which means that numbers that fit the selection will be eliminated. Also similar filters are grouped together to reduce explanation redundancy.

Following you will find the list of all Filter Functions:

 [SELECT SUMS][SELECT SUMS AB][SELECT SUMS AC][SELECT SUMS AD][SELECT SUMS BC][SELECT SUMS BD][SELECT SUMS CD][SELECT SUMS ABC][SELECT SUMS ABD][SELECT SUMS ACD][SELECT SUMS BCD] This filter finds numbers that have the sums that you request. In the Pick 4 game the largest sum is 36 (for the 9999: 9+9+9+9=36) and 0 for the lowest sum (0000; 0+0+0+0=0). Your entry options are numbers between 0 and 36.The filters below the first one only look at the 6 possible pair locations (entry options are 0 to 18) and the 4 possible triplet positions (entry options are 0 to 27).
 [SELECT CUT SUMS][SELECT CUT SUMS AB][SELECT CUT SUMS AC][SELECT CUT SUMS AD][SELECT CUT SUMS BC][SELECT CUT SUMS BD][SELECT CUT SUMS CD][SELECT CUT SUMS ABC][SELECT CUT SUMS ABD][SELECT CUT SUMS ACD][SELECT CUT SUMS BCD] Based on the SUM selection this filter uses only the last digit of the sum of the numbers for comparison. For example 4567 (4+5+6+7=22) has the CUT SUM of 2 (the last digit from the sum 22). Entry options here are 0 1 2 3 4 5 6 7 8 9.The filters below the first one only look at the 6 possible pair and the 4 possible triplet positions.
 [SELECT ROOTS][SELECT ROOTS AB][SELECT ROOTS AC][SELECT ROOTS AD][SELECT ROOTS BC][SELECT ROOTS BD][SELECT ROOTS CD][SELECT ROOTS ABC][SELECT ROOTS ABD][SELECT ROOTS ACD][SELECT ROOTS BCD] Also based on the SUM selection the ROOTS filter – also knows as root sums - is the sum of the sum adding up the numbers until only one digit is left. For example 4567 (4+5+6+7=22 2+2=4) has the Root of 4 (the sum of the initial sum 22). Entry options here are 0 1 2 3 4 5 6 7 8 9.The filters below the first one only look at the 6 possible pair and the 4 possible triplet positions.
 [SELECT LINE WIDTH][SELECT LINE WIDTH AB][SELECT LINE WIDTH AC][SELECT LINE WIDTH AD][SELECT LINE WIDTH BC][SELECT LINE WIDTH BD][SELECT LINE WIDTH CD][SELECT LINE WIDTH ABC][SELECT LINE WIDTH ABD][SELECT LINE WIDTH ACD][SELECT LINE WIDTH BCD] This filter looks at the difference between the highest and the lowest digit within a number. For example 4567 (lowest digit 4, highest digit 7: 7-4=3) has the line width of 3; the difference the highest digit 7 and the lowest digit 4. Your entry choices are 0 1 2 3 4 5 6 7 8 9.The filters below the first one only look at the 6 possible pair and the 4 possible triplet positions.
 [SELECT TYPES] With this filter you are selecting the 5 types of numbers possible within the Pick 4 game: SINGLES (all digits are different: 3567), DOUBLES (two digits of the number are equal: 3557), 2DOUBLES (2 equal pairs are in the number: 3553), TRIPLES (three digits are the same: 3337), QUADRUPLES (all digits are the same: 3333). So your entry options are: SINGLES DOUBLES 2DOUBLES TRIPLES and QUADRUPLES.
 [SELECT HIGH LOW][SELECT HIGH LOW BOXED] These filters allow you the select numbers based on high and low digits within the number. HIGH digits (H) are 5 6 7 8 9 and LOW digits (L) are 0 1 2 3 4. The first selection looks at the number on a positional level, meaning the position of the high and low numbers is of importance. There are 16 options possible for this selection:HHHH, HHHL, HHLH, HHLL, HLHH, HLHL, HLLH, HLLL, LHHH, LHHL, LHLH, LHLL, LLHH, LLHL, LLLH, LLLL.The second filter only looks at the number as a whole, meaning how many digits are high and how many are low. That reduces the choices to the following 5: HHHH, HHHL, HHLL, HLLL, LLLL.
 [SELECT EVEN ODD][SELECT EVEN ODD BOXED] These filters allow you the select numbers based on even and odds digits within the number. EVEN digits (E) are 0 2 4 6 8 and ODD digits (O) are 1 3 5 7 9. The first selection looks at the number on a positional level, meaning the position of the high and low numbers is of importance. There are 16 options possible for this selection:EEEE, EEEO, EEOE, EEOO, EOEE, EOEO, EOOE, EOOO, OEEE, OEEO, OEOE, OEOO, OOEE, OOEO, OOOE, OOOO.The second filter only looks at the number as a whole, meaning how many digits are even and how many are odd. That reduces the choices to the following 5: EEEE, EEEO, EEOO, EOOO, OOOO.

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