Combinations Generator for n/N + 1/M Games

Multi-number lottery games with two set of numbers, where only one number is picked from the second set are refered to as n/N + 1/M games. That is, the player selects n numbers from the first set of numbers ranging rom 1 to N, and one number from the second set from 1 to M, where N and M are established by the type of lottery game. A common example is the US Mega Millions lottery which is represented by 5/56 + 1/46, where the player selects 5 numbers from 1 to 56 plus a Mega Ball from 1 to 46.

This lottery utility generates all the combinations of a given number of numbers (let's call it k) into groups of n numbers combined with one of the j numbers of the second set. Suppose you want to play all the possible combinations of the Mega Million numbers that are divisible 3, of both sets. That is 3,6,9,12,15,etc. Then k will be 18 since there are 18 numbers divisible by 3 in the numbers 1 to 56, and j will be 15 (in the second set 1 to 46). All the possible combinations of these 18 and 15 numbers into groups of 5 numbers and an extra ball will be 128,520. Even for a lottery pool this number of lottery tickets is one too many to play. Also, it will be too much work for our server to generate so many combinations.

We have therefore to limit the number of combinations to be generated to about 200,000. Yes, you can generate those 128K combinations since the the number is below our set limit. For higher combinations, you can use the following combinations calculator to see how many combinations there are for a given n and k. It will also tell you if you can generate the combinations using our utility.

If you get the "Yes you can" answer in the above test, the next step is to use the generator itself. The combinations generator can be used for any multi-number lottery game, with two set of numbers, as long as the total numbers to select from (N) do not exceed 100 for each set, and n is 10 or less. This, we hope, will cover any such type of lottery game in the world.

To initiaze the generator, please specify the type lottery game by entering the values of n, N, and M below. For example, for a 4/44 + 1/22 game, n=4, N=44, and M=22