How many tickets for all 2-combinations?

[SoftwareTester]

I would like to know how many tickets are needed to have all possible combinations of TWO balls covered when you have 49 balls.
Prefereable all numbers should occur about the same number of times (difference between max and min being 1 ball)

 

[zerro]

1176 Combination's, Each number appears 48 Times
# Appears Percentage
1 48 2.04
2 48 2.04
3 48 2.04
4 48 2.04
5 48 2.04
6 48 2.04
7 48 2.04
8 48 2.04
9 48 2.04
10 48 2.04
11 48 2.04
12 48 2.04
13 48 2.04
14 48 2.04
15 48 2.04
16 48 2.04
17 48 2.04
18 48 2.04
19 48 2.04
20 48 2.04
21 48 2.04
22 48 2.04
23 48 2.04
24 48 2.04
25 48 2.04
26 48 2.04
27 48 2.04
28 48 2.04
29 48 2.04
30 48 2.04
31 48 2.04
32 48 2.04
33 48 2.04
34 48 2.04
35 48 2.04
36 48 2.04
37 48 2.04
38 48 2.04
39 48 2.04
40 48 2.04
41 48 2.04
42 48 2.04
43 48 2.04
44 48 2.04
45 48 2.04
46 48 2.04
47 48 2.04
48 48 2.04
49 48 2.04

 

[johnph77]

There are 1,128 pairs possible for numbers between 1 and 49.

 

[CMF]

I'm not aware of a 6/49 game that pays on a Two win.

The Cover for 2 if 2 in 49 is given as 82 on Weef's website albeit with lots of repeat Twos.

Without repeat Twos you can do a 48 Comb Cover that will give you a non paying Two hit every draw.

Colin Fairbrother

 

[zerro]

There are 1,128 pairs possible for numbers between 1 and 49.

The equation is 48*49/2*1 = 1176
The last few lines of the combination's with the counter below, created with a combination plugin.

841-23 39 ~ 842-23 40 ~ 843-23 41 ~ 844-23 42 ~ 845-23 43 ~ 846-23 44 ~ 847-23 45 ~ 848-23 46 ~ 849-23 47 ~ 850-23 48
851-23 49 ~ 852-24 25 ~ 853-24 26 ~ 854-24 27 ~ 855-24 28 ~ 856-24 29 ~ 857-24 30 ~ 858-24 31 ~ 859-24 32 ~ 860-24 33
861-24 34 ~ 862-24 35 ~ 863-24 36 ~ 864-24 37 ~ 865-24 38 ~ 866-24 39 ~ 867-24 40 ~ 868-24 41 ~ 869-24 42 ~ 870-24 43
871-24 44 ~ 872-24 45 ~ 873-24 46 ~ 874-24 47 ~ 875-24 48 ~ 876-24 49 ~ 877-25 26 ~ 878-25 27 ~ 879-25 28 ~ 880-25 29
881-25 30 ~ 882-25 31 ~ 883-25 32 ~ 884-25 33 ~ 885-25 34 ~ 886-25 35 ~ 887-25 36 ~ 888-25 37 ~ 889-25 38 ~ 890-25 39
891-25 40 ~ 892-25 41 ~ 893-25 42 ~ 894-25 43 ~ 895-25 44 ~ 896-25 45 ~ 897-25 46 ~ 898-25 47 ~ 899-25 48 ~ 900-25 49
901-26 27 ~ 902-26 28 ~ 903-26 29 ~ 904-26 30 ~ 905-26 31 ~ 906-26 32 ~ 907-26 33 ~ 908-26 34 ~ 909-26 35 ~ 910-26 36
911-26 37 ~ 912-26 38 ~ 913-26 39 ~ 914-26 40 ~ 915-26 41 ~ 916-26 42 ~ 917-26 43 ~ 918-26 44 ~ 919-26 45 ~ 920-26 46
921-26 47 ~ 922-26 48 ~ 923-26 49 ~ 924-27 28 ~ 925-27 29 ~ 926-27 30 ~ 927-27 31 ~ 928-27 32 ~ 929-27 33 ~ 930-27 34
931-27 35 ~ 932-27 36 ~ 933-27 37 ~ 934-27 38 ~ 935-27 39 ~ 936-27 40 ~ 937-27 41 ~ 938-27 42 ~ 939-27 43 ~ 940-27 44
941-27 45 ~ 942-27 46 ~ 943-27 47 ~ 944-27 48 ~ 945-27 49 ~ 946-28 29 ~ 947-28 30 ~ 948-28 31 ~ 949-28 32 ~ 950-28 33
951-28 34 ~ 952-28 35 ~ 953-28 36 ~ 954-28 37 ~ 955-28 38 ~ 956-28 39 ~ 957-28 40 ~ 958-28 41 ~ 959-28 42 ~ 960-28 43
961-28 44 ~ 962-28 45 ~ 963-28 46 ~ 964-28 47 ~ 965-28 48 ~ 966-28 49 ~ 967-29 30 ~ 968-29 31 ~ 969-29 32 ~ 970-29 33
971-29 34 ~ 972-29 35 ~ 973-29 36 ~ 974-29 37 ~ 975-29 38 ~ 976-29 39 ~ 977-29 40 ~ 978-29 41 ~ 979-29 42 ~ 980-29 43
981-29 44 ~ 982-29 45 ~ 983-29 46 ~ 984-29 47 ~ 985-29 48 ~ 986-29 49 ~ 987-30 31 ~ 988-30 32 ~ 989-30 33 ~ 990-30 34
991-30 35 ~ 992-30 36 ~ 993-30 37 ~ 994-30 38 ~ 995-30 39 ~ 996-30 40 ~ 997-30 41 ~ 998-30 42 ~ 999-30 43 ~ 1000-30 44
1001-30 45 ~ 1002-30 46 ~ 1003-30 47 ~ 1004-30 48 ~ 1005-30 49 ~ 1006-31 32 ~ 1007-31 33 ~ 1008-31 34 ~ 1009-31 35 ~ 1010-31 36
1011-31 37 ~ 1012-31 38 ~ 1013-31 39 ~ 1014-31 40 ~ 1015-31 41 ~ 1016-31 42 ~ 1017-31 43 ~ 1018-31 44 ~ 1019-31 45 ~ 1020-31 46
1021-31 47 ~ 1022-31 48 ~ 1023-31 49 ~ 1024-32 33 ~ 1025-32 34 ~ 1026-32 35 ~ 1027-32 36 ~ 1028-32 37 ~ 1029-32 38 ~ 1030-32 39
1031-32 40 ~ 1032-32 41 ~ 1033-32 42 ~ 1034-32 43 ~ 1035-32 44 ~ 1036-32 45 ~ 1037-32 46 ~ 1038-32 47 ~ 1039-32 48 ~ 1040-32 49
1041-33 34 ~ 1042-33 35 ~ 1043-33 36 ~ 1044-33 37 ~ 1045-33 38 ~ 1046-33 39 ~ 1047-33 40 ~ 1048-33 41 ~ 1049-33 42 ~ 1050-33 43
1051-33 44 ~ 1052-33 45 ~ 1053-33 46 ~ 1054-33 47 ~ 1055-33 48 ~ 1056-33 49 ~ 1057-34 35 ~ 1058-34 36 ~ 1059-34 37 ~ 1060-34 38
1061-34 39 ~ 1062-34 40 ~ 1063-34 41 ~ 1064-34 42 ~ 1065-34 43 ~ 1066-34 44 ~ 1067-34 45 ~ 1068-34 46 ~ 1069-34 47 ~ 1070-34 48
1071-34 49 ~ 1072-35 36 ~ 1073-35 37 ~ 1074-35 38 ~ 1075-35 39 ~ 1076-35 40 ~ 1077-35 41 ~ 1078-35 42 ~ 1079-35 43 ~ 1080-35 44
1081-35 45 ~ 1082-35 46 ~ 1083-35 47 ~ 1084-35 48 ~ 1085-35 49 ~ 1086-36 37 ~ 1087-36 38 ~ 1088-36 39 ~ 1089-36 40 ~ 1090-36 41
1091-36 42 ~ 1092-36 43 ~ 1093-36 44 ~ 1094-36 45 ~ 1095-36 46 ~ 1096-36 47 ~ 1097-36 48 ~ 1098-36 49 ~ 1099-37 38 ~ 1100-37 39
1101-37 40 ~ 1102-37 41 ~ 1103-37 42 ~ 1104-37 43 ~ 1105-37 44 ~ 1106-37 45 ~ 1107-37 46 ~ 1108-37 47 ~ 1109-37 48 ~ 1110-37 49
1111-38 39 ~ 1112-38 40 ~ 1113-38 41 ~ 1114-38 42 ~ 1115-38 43 ~ 1116-38 44 ~ 1117-38 45 ~ 1118-38 46 ~ 1119-38 47 ~ 1120-38 48
1121-38 49 ~ 1122-39 40 ~ 1123-39 41 ~ 1124-39 42 ~ 1125-39 43 ~ 1126-39 44 ~ 1127-39 45 ~ 1128-39 46 ~ 1129-39 47 ~ 1130-39 48
1131-39 49 ~ 1132-40 41 ~ 1133-40 42 ~ 1134-40 43 ~ 1135-40 44 ~ 1136-40 45 ~ 1137-40 46 ~ 1138-40 47 ~ 1139-40 48 ~ 1140-40 49
1141-41 42 ~ 1142-41 43 ~ 1143-41 44 ~ 1144-41 45 ~ 1145-41 46 ~ 1146-41 47 ~ 1147-41 48 ~ 1148-41 49 ~ 1149-42 43 ~ 1150-42 44
1151-42 45 ~ 1152-42 46 ~ 1153-42 47 ~ 1154-42 48 ~ 1155-42 49 ~ 1156-43 44 ~ 1157-43 45 ~ 1158-43 46 ~ 1159-43 47 ~ 1160-43 48
1161-43 49 ~ 1162-44 45 ~ 1163-44 46 ~ 1164-44 47 ~ 1165-44 48 ~ 1166-44 49 ~ 1167-45 46 ~ 1168-45 47 ~ 1169-45 48 ~ 1170-45 49
1171-46 47 ~ 1172-46 48 ~ 1173-46 49 ~ 1174-47 48 ~ 1175-47 49 ~ 1176-48 49

 

[CMF]

My understanding of this thread is as follows:

1. SoftwareTester asked for the Cover C(49,6,2,2) which I wrote is 82 at Weef's site and is down loadable there.

2. Zero gave a list of 49 pairs with 1 integer appearing 49 times and the rest once. Nothing wrong with this apart from it not satisfying SoftwareTester's requirement that the appearance of each integer be the same.

3. Johnph77 interpreted Zero's list as being the cue to recite some basic knowledge about the combinations of two integers from 49.

4. The accurate reply I gave served as a bump cue for Johnph77 to enumerate in a rather messy way the combinations of 2 integers from 49.

If you have some desire to enumerate the Combinations of 2 integers from 49 and are unable to write the simple code yourself (do a search - it's in these forums more than once) then a freely available tool is Covermaster. Set your parameters to Pool 49, Pick (whatever), Match 2 and Hits 2. (Covermaster only shows in the grid combinations from 3 to 7.) You will notice the value in To Test as 1176 which is the number of combination of 2 integers from 49 integers which can be calculated by 49!/((49-2)! x 2!)=(49 x 48)/2. Click on Test and change the Max Entries to 1176. Close click on Test again and you have the 1176 combinations of 2 enumerated. Click on To Clipboard and you can then paste it into Notepad, Excel, Access whatever to give the enumeration below:-

ID P1 P2
1 01 02
2 01 03
3 01 04
4 01 05
5 01 06
6 01 07
7 01 08
8 01 09
9 01 10
10 01 11
11 01 12
12 01 13
13 01 14
14 01 15
15 01 16
16 01 17
17 01 18
18 01 19
19 01 20
20 01 21
21 01 22
22 01 23
23 01 24
24 01 25
25 01 26
26 01 27
27 01 28
28 01 29
29 01 30
30 01 31
31 01 32
32 01 33
33 01 34
34 01 35
35 01 36
36 01 37
37 01 38
38 01 39
39 01 40
40 01 41
41 01 42
42 01 43
43 01 44
44 01 45
45 01 46
46 01 47
47 01 48
48 01 49
49 02 03
50 02 04
etc

Regards
Colin Fairbrother

 

[CMF]

Correction:

"2. Zero gave a list of 49 pairs with 1 integer appearing 49 times and the rest once."

There is something wrong there - the 48th line duplicates integer 48!

My subconscious recognized it - eventually it surfaced to advise me that was impossible.

Regards
Colin Fairbrother

 

[johnph77]

I also was in error - there are 1,176 possible pairs of the integers between 1 and 49. Sorry if anyone was inconvenienced.

 

[zerro]

Each number is represented 48 times
# Appears Percentage
48 48 2.04
1 to 49 = 48 number 1s when all combos have completed
48 is the same, there will be 48 48s also.

 

[CMF]

Correction # 2: The messy enumeration was by Zerro not Johnph77 - sorry.

Getting back to the original question as I said Weef's website has the COVER, which is what SoftwareTester was asking for, in 82 lines with 48 integers repeated 10 times and 1 repeated 12 times. For the difference between the max and min repetition to be 1 you would have to play around with the Cover. Personally, I attach no importance to so called "balancing" of the integers as 1 or 2 integers don't pay - so, your starting point is the Threes. The important point to me is that 18 of the paying Three prizes are repeated twice.

Colin Fairbrother