20200916 (Wednesday)

5

Integer sequences

The On-Line Encyclopedia of Integer Sequences (OEIS)

(1). Integer sequences.

One day, several months ago, I typed in the search box of Google, the following: 1, 7, 28, 84, 210, [five numbers], and Google "took me" to the website of The OEIS (The On-Line Encyclopedia of Integer Sequences). The institution was founded in 1964 by British-American mathematician N.J.A. Sloane.

The OEIS

Neil James Alexander Sloane (Beaumaris, Wales, 1939- ) is still very active.

Now, where did the above-mentioned numbers 1, 7, 28, 84, and 210 come from?

Well, in Mexico there are several lotteries similar to the U.S. Lotto. One of them is named "Melate* Retro" (it is played twice a week, on Tuesdays and Saturdays).

(*Melate is a word arbitrarily "composed" out of two words —me late—... their meaning is kind of "I have a feeling", "it seems to me", "my heart beats to me", "my heart ❤️ is telling me that...".)

The Melate Retro has a total of 39 numbers, from 1 to 39. You win the jackpot (the first prize) if your selection of six numbers matches the six numbers drawn from the six revolving drums of a tombola.

Now, you can select different combinations; id est, you can select not only 6 numbers, but 7 (this combo will cost you 7× [1 × 7]), or 8 (this combo will cost you 28× [7 × 4]), or 9 (this combo will cost you 84× [28 × 3]), or 10 (this combo will cost you 210× [84 × 2.5]), and so on.

Now you and I know where those five numbers came from, but the really interesting thing is that such integer sequence may have multiple origins, as this web page of The OEIS informs us.

(2). The odds.

Now, the odds of winning the jackpot in the Melate Retro can be calculated as follows:

(A). Firstly, you have to multiply the six biggest numbers of the 1-39 group: 39 × 38 × 37 × 36 × 35 × 34 = 2 349 088 560

(B). Then you have to calculate the factorial of 6: 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.

(C). After that, you should divide the result of A by the result of B: 2349088560/720 = 3 262 623.

So, your odds of winning the first prize in the Melate Retro are 1 in 3262623.

Also, you can check the result for the number 39 at result for the number 39

20200916 (Wednesday)