### Kannappan Sampath

Shared publicly -This is for general audience Peter Keevash's work on designs...

**"Design theory may even have been used by betting cartels that made millions of dollars off of Massachusetts’ poorly designed Cash WinFall lottery**between 2005 and 2011. That lottery involved choosing six numbers out of 46 choices; tickets won a jackpot if they matched all six numbers, and smaller prizes if they matched five out of six numbers.

There are more than 9 million possible ways to pick six numbers out of 46, so buying tickets with every possible combination would cost far more than the game’s typical jackpot. A number of groups realized, however, that buying hundreds of thousands of tickets would enable them to turn a profit by scooping up many of the smaller prizes. Arguably the best assortment of tickets for such a strategy is a (46, 6, 5) design, which creates tickets of six numbers such that every set of five numbers appears exactly once, guaranteeing either the jackpot or every possible five-number prize.

No one has found a (46, 6, 5) design so far, Colbourn said, but designs exist that are close enough to be useful. Did any of the betting cartels use such a design “to siphon money from the Lottery at no risk to themselves?” wrote Jordan Ellenberg, a mathematician at the University of Wisconsin, Madison, who discussed the Cash WinFall lottery in his book How Not to Be Wrong. If they didn’t, Ellenberg wrote, they probably should have. [...]"

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A 150-year-old conundrum about how to group people has been solved, but many puzzles remain.

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