Let me count the ‘ways’ of keno tickets

January 17, 2001 3:14 AM
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When way tickets start to get complicated, calculating the possible ways to play on the ticket can start to get complicated too. Even relatively simple tickets like we have dealt with in the last few weeks can be difficult to compute.

Here is one simple way to calculate the ways on any ticket. Suppose we have a ticket marked with 15 spots, grouped 4-4-4-1-1-1. The first step is to take the first group and write it down:

4

The second step is to add the second group to the first, and copy the results:

4+4=8

The third step is to add the third group to the results above, and copy the total results to the column:

4+4=8+4=12

We then add the next group to the results, and proceed as above, adding the group of 1 to all previous results:

4+1=5
4+1=5
8+1=9
4+1=5
8+1=9
8+1=9
12+1=13

Next we follow the same procedure with the 2nd group of 1:

4+1=5
4+1=5
8+1=9
4+1=5
8+1=9
8+1=9
12+1=13
1+1=2
5+1=6
5+1=6
9+1=10
5+1=6
9+1=10
9+1=10
13+1=14

For the last step, we take the final group of 1 and add it to all previous results:

4+1=5
4+1=5
8+1=9
4+1=5
8+1=9
8+1=9
12+1=13
1+1=2
5+1=6
5+1=6
9+1=10
5+1=6
9+1=10
9+1=10
13+1=14
1+1=2
5+1=6
5+1=6
9+1=10
5+1=6
9+1=10
9+1=10
13+1=14
2+1=3
6+1=7
6+1=7
10+1=11
6+1=7
10+1=11
10+1=11
14+1=15

Now, having completed this simple task of repetitive addition, we can see that there are 63 ways on this ticket, to wit: A one way 15, a 3 way 14, a 3 way 13, a 1 way 12, a three way 11, a 9 way 10, a 9 way 9, a 3 way 8, a 3 way 7, a 9 way 6, a 9 way 5, a 3 way 11, a 1 way 3, a three way 2 and a 3 way 1.

Simple, eh?

Well, that’s it for now, good luck, I’ll see you in line!