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Lottery Range Ticket

Covers all combinations of numbers from X to Y, inclusive
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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- combinations.

First, let's note that lottery drawings tend to come in two basic types. One type has several sets of identical numbers; the other type has just one set of all-different numbers. Range Tickets can work for either, although the second type is a bit trickier, in terms of computing the actual quantity of number-combinations covered.

For the several sets of identical numbers, the lottery officials have several machines each containing the same set of numbers, usually Zero to Nine. If there are three machines, then the total number of combinations that can be picked range from 000 to 999, one thousand, that is. An example Range Ticket could have the numbers 123 and 567 on it, and you would be covering 567- 123+1 (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 charged appropriately.

For the single set of all-different numbers, the lottery officials use a single machine from which several numbers are picked. The numbers might range from 1 to 50. Here the smallest numbers that could appear on a winning ticket (assuming 5 numbers picked) 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. (If 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 are 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 some 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. However, 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 Range 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).

Vernon, Jan 09 2016

BOTEC https://www.allacronyms.com/BOTEC
Back of the envelope calculation [Vernon, Jan 09 2016]

Actual case where a group tried to cover all the bets http://www.nytimes....html?pagewanted=all
As implied by the main text and an annotation. [Vernon, Jan 09 2016]

Number Bases http://mathbits.com...oduction/Nbases.htm
Just in case you need help to think in terms of Base 50 [Vernon, Jan 09 2016]

[link]






       I also suspect the billionaires all know each other, and could easily form a pool, such that 20 of them only spend 5 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 machine to churn out up to 46 individual tickets?
Vernon, Jan 09 2016
  

       A great way to extract more cash from people who have an inadequate understanding of probability. [+]
pocmloc, Jan 09 2016
  

       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.   

       I woke up mean today.
not_morrison_rm, Jan 10 2016
  
      
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