The ‘everything’ keno ticket

June 11, 2001 12:40 AM
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This week’s entry in the favorite ticket derby I whimsically call the “Everything Ticket,” because it has exactly one of every way on it from a 15 spot down to a one spot. The ticket is marked using 15 numbers, grouped 8-4-2-1. (See the illustration.) This is the only way to do this, there is no other combination/way ticket that has exactly one of each way. A lot of Keno checkers would scratch their heads in wonderment at the task ahead of them when they ran across it in their “book.” On closer inspection, though, the ticket is not that hard to check. For instance, suppose you hit a total of eight out of 15, with a five out of eight, a one out of four, a solid deuce, and a blank on the king (one spot.) To check the ticket, it is enough to merely write down the groups with the respective catches underneath:

8 4 2 1

5 1 2 0

The checker can see by inspection that there is an eight out of 15. By covering up the one spot, he can see that there is also an eight out of 14. Similarly, by covering the deuce, he can see that there is a five out of 13, and by covering the 2+1 there is a six out of 12. By covering the four spot and the eight spots he can see that there are respectively a seven out of 11 and a three out of seven. Taking the eight spot by itself, there is a five out of eight. Taking the 8+1, there is a five out of nine. Taking the 8+2, there is a seven out of 10. Taking the 4+2, there is a three out of six, and taking the 4+1, there is a one out of five. Finally, there is a one out of four, a two out of three, a two out of two, and a zero out of one. The check is done!