Fingers and Toes, Here We Go!
Number systems adopted by people over the centuries have been based most often on the number of fingers and toes humans have evolved, but not all. Notable exceptions are the modern ones based on binary digits which are useful in the world of on/off conditions in electronic computers. For computational efficiency, before computers, a base Twelve system would have been a better choice for us than Ten. This article discusses the Base Twelve or Duodecimal system as well as the peoples who have and still use it. If you're interested, you can find similar information on other systems.
http://en.wikipedia.org/wiki/Duodecimal
"Languages using duodecimal number systems are uncommon. Languages in the Nigerian Middle Belt such as Janji, Gbiri-Niragu (Kahugu), the Nimbia dialect of Gwandara[1]; the Chepang language of Nepal[2] and the Mahl language of Minicoy Island in India are known to use duodecimal numerals. In fiction, J. R. R. Tolkien's Elvish languages used duodecimal."
For purposes of discussion, I've adopted the tradition of using our familiar base TEN numerals, [0,1,2,3,4,5,6,7,8,9] to represent the same number of objects for all the bases listed, except for the Roman System. For non-Roman bases larger than TEN, I will use [A,B,C,D,E,F,G,H,J,K] to count beyond 9 with a single digit. Also, when there is a possibility of confusion, I will append the BASE of a number in parenthesis (using base TEN digits.)
The (5,39(10)) Lotto is preferred by many of the proponents of lottery selection systems based on the counting of digits. Therefore, I've compiled a table of what the Labels for each of the 39(10) objects in this game would look like in systems of various BASES.
BASE BASE BASE BASE BASE BASE BASE ROMAN
TEN TWO FOUR EIGHT TWELVE SIXTEEN *TWENTY NUMERALS
01 000001 001 01 01 01 01 I
02 000010 002 02 02 02 02 II
03 000011 003 03 03 03 03 III
04 000100 010 04 04 04 04 IV
05 000101 011 05 05 05 05 V
06 000110 012 06 06 06 06 VI
07 000111 013 07 07 07 07 VII
08 001000 020 10 08 08 08 VIII
09 001001 021 11 09 09 09 IX
10 001010 022 12 0A 0A 0A X
11 001011 023 13 0B 0B 0B XI
12 001100 030 14 10 0C 0C XII
13 001101 031 15 11 0D 0D XIII
14 001110 032 16 12 0E 0E XIV
15 001111 033 17 13 0F 0F XV
16 010000 100 20 14 10 0G XVI
17 010001 101 21 15 11 0H XVII
18 010010 102 22 16 12 0J XVIII
19 010011 103 23 17 13 0K XIX
20 010100 110 24 18 14 10 XX
21 010101 111 25 19 15 11 XXI
22 010110 112 26 1A 16 12 XXII
23 010111 113 27 1B 17 13 XXIII
24 011000 120 30 20 18 14 XXIV
25 011001 121 31 21 19 15 XXV
26 011010 122 32 22 1A 16 XXVI
27 011011 123 33 23 1B 17 XXVII
28 011100 130 34 24 1C 18 XXVIII
29 011101 131 35 25 1D 19 XXIX
30 011110 132 36 26 1E 1A XXX
31 011111 133 37 27 1F 1B XXXI
32 100000 200 40 28 20 1C XXXII
33 100001 201 41 29 21 1D XXXIII
34 100010 202 42 2A 22 1E XXXIV
35 100011 203 43 2B 23 1F XXXV
36 100100 210 44 30 24 1G XXXVI
37 100101 211 45 31 25 1H XXXVII
38 100110 212 46 32 26 1J XXXVIII
39 100111 213 47 33 27 1K XXXIX
* Yup'ik of South Alaska.
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I think this is enough to digest for the time being. I hope you will ask yourself questions regarding what the information above should indicate to anyone counting digits to choose lottery numbers. Keep in mind that the ping pong balls will NOT be aware of what base was used to prepare their label, and consequently, will be clueless regarding what digits they are wearing! Another pertinent question might be, "How will the distribution of frequency counts of digits change for the 575757(10) combinations of 5?" This is important, as digit selection proponents select and reject sets based on this distribution.
Remember, if we had evolved with 3 or 4 fingers, we very likely would be using a 6, 8, or 12(10) based number system today, rather than TEN!