Fwd: Lotto and Good Will Hunting

Sanderson Smith (Sanderson_Smith@cate.org)
Tue, 14 Apr 1998 17:47:25 -0800

Hi group... below is a note I put in the e-mail faculty folder at Cate School.
Perhaps you will find it of some interest.
-Keep smiling, all.

Some (perhaps)interesting tidbits on CALIFORNIA LOTTO and GOOD WILL HUNTING.
As you may know, there was recently a rush to buy LOTTO tickets as the jackpot amount got extremely large. Three different
groups shared this jackpot as a result of "hitting it big" last week. In California Lotto, one picks 6 numbers from the set
1,2,3,...., 49,50,51. The State then randomly picks 6 numbers. If you match all 6, you make big bucks. Some interesting
mathematical facts about California Lotto:

The number of six number combinations is 18,009,460.
If you wanted to fill out 18,009,460 cards to cover all number combinations, and, if you
could fill out cards at the rate of one card per second, it would take you 208 days to
complete the task.
If you buy fifty Lotto tickets a week, you can expect to win the jackpot once every five
thousand years.
If you purchased two Lotto tickets a week for 110,000 years, you would have a 50%
chance of winning the jackpot once during that period of time.

Interestingly, there are people who make money selling books and software containing ways to increase your chances of
winning. Some advertise things like "technique will increase your chances of winning by 100%." Of course, a great way to
increase your chances of winning by 100% is to buy two tickets instead of one.
In this movie, Will is actually compared to Srinivasa Ramanujan (1887-1920), who was born in the town of Kumbakonam in
Southern India.

Incredibly, Ramanujan's work was not well known until 1976, when 130 pages of his scribbled materials were discovered in a
box of letters and bills in the library of Trinity College in Cambridge. This material is now known as the LOST NOTEBOOK.
This source, and other papers of Ramanujan, contain thousands of formulas, almost always without proof or even a hint of
where they came from.

Between 1903 and 1914, the unknown and self-educated Ramanujan filled three notebooks with mathematical formulas and
relationships. Since he could not afford to buy paper, he did most of his computations and experimentation on a slate,
erasing all his intermediate work and recording only his final results.

Ramanujan was "discovered" by the great English mathematican, G. H. Hardy (1877-1947). Hardy brought Ramanujan to England,
but the young Indian genius could not adjust to the new climate, became ill, and died at an early age. Remember the
professor looking at Will's work on the chalkboard in Good Will Hunting? In referencing Ramanujan's formulas, Hardy wrote
"I have never seen anything like them. A single look at them is enough to show that they could only be written down by a
mathematician of the highest class. They must be true because, if they were not, no one would have to imagination to invent

Modern mathematicians and scientists have used Ramanujan's discoveries in multiple areas, including computer technology.
One wonder's what Ramanujan would have been able to accomplish had he lived to have access to modern computers. It is
generally accepted that Ramanujan's thinking was many decades ahead of his time.

Many of Ramanujan's intriguing assertions have yet to be proved. As modern mathematicians have worked toward uncovering the
processes leading to his perceptive statements of theorems, they have discovered new and useful mathematical techniques and
methods. Ramanujan's legacy will keep today's mathematicians and scientists busy for many years to come.

Again, the name Ramanujan is stated multiple times in the movie Good Will Hunting.