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This is a simple way to either waste a lot of money on a lottery,
or to guarantee-win it, provided you HAVE enough money to pay
in advance!, of course!-- for that Range Ticket. In either case,
you only need to buy one ticket to cover a lot of number-
First, let's note that
lottery drawings tend to come in two basic
types. One type has several sets of identical numbers; the
type has just one set of all-different numbers. Range Tickets
work for either, although the second type is a bit trickier, in
terms of computing the actual quantity of number-combinations
For the several sets of identical numbers, the lottery officials
have several machines each containing the same set of
usually Zero to Nine. If there are three machines, then the
number of combinations that can be picked range from 000 to
one thousand, that is. An example Range Ticket could have the
numbers 123 and 567 on it, and you would be covering 567-
(because we want the chosen range to always include the end-
point numbers, else HOW could you pick the entire 000-999
range?), or 445 combinations of numbers, and you would be
For the single set of all-different numbers, the lottery officials
use a single machine from which several numbers are picked.
numbers might range from 1 to 50. Here the smallest numbers
that could appear on a winning ticket (assuming 5 numbers
would be 1,2,3,4,5, not necessarily in that order. If the Range
Ticket had these two sets of numbers on it, 1,2,3,4,5 and
2,3,4,5,6 --you would be covering a quite large range (over 5
million combinations, by my quick BOTEC).
Figuring it precisely is a bit tricky because combinations of
numbers like 2,3,4,5,5 cannot happen in the drawing, but could
too-easily be included in the computation of the valid
combinations. We CAN note that the "smallest" number
combination is 1,2,3,4,5 while the "largest" is 50,49,48,47,46.
you can think in terms of "Base 50" the reasoning behind that
statement should be clear.) Modern computers are perfectly
suited for the task of figuring exactly how many combinations
included in any chosen range, once appropriate software is
written. Since I'm not planning on writing that software, that
suffices for this Idea to qualify as "Half Baked".
I'm quite aware that this Idea would make it far too easy for
rich dude to buy the whole range of numbers, whenever some
prize-progression type of lottery
reaches the size where the payout could cover the cost.
that rich dude probably isn't the only one thinking about doing
that! It could be really entertaining to the general population if
20 billionaires spent a hundred million dollars each on Full
Tickets, because the prize was half-a-billion dollars, --and then
the prize had to be split 20 different ways (or more if there was
also a random winner who only spent one dollar).
Back of the envelope calculation [Vernon, Jan 09 2016]
Actual case where a group tried to cover all the bets
As implied by the main text and an annotation. [Vernon, Jan 09 2016]
Just in case you need help to think in terms of Base 50 [Vernon, Jan 09 2016]
||I also suspect the billionaires all know each other, and
could easily form a pool, such that 20 of them only
million dollars each, to buy a single hundred-megabuck
Full Range Ticket (when THAT happens to be the max
for this type of lottery). But
the Idea still makes it easy for anyone to buy a smaller
Range Ticket, such as 1,2,3,4,5 through 1,2,3,4,50 (46
combinations), which just might include the winning
combination. Would you rather wait for the ticket
to churn out up to 46 individual tickets?
||A great way to extract more cash from people who have an inadequate understanding of probability. [+]
||I was thinking this could be more like, you put
down a thousand [insert local currency ], your
ticket is pinned to the back of politician, and
you get to win if you can hit the ticket, with the
gatling gun and unlimited ammo provided.