0
$\begingroup$

I am interested what type of combinatorics is using for following bookmakers system called "S3":

  1. We have N={1..8} events
  2. We build express pairs C=8 like

    [(1, 2, 4), (1, 3, 6), (1, 6, 8), (2, 3, 5), (2, 5, 8), (3, 7, 8), (4, 5, 7), (4, 6, 7)]

Each event repeats 3-times: 1 => (1, 2, 4), (1, 3, 6), (1, 6, 8)..

It's not permutation, combination... Please advice what is it?

I want as example generate in similar way 4 from 10 if this possible. After I'd like to predict the optimal way for building the `pairs'

$\endgroup$
1
$\begingroup$

This can be interpreted as an unusual error correcting code with a non-binary signal.

Essentially, you want the tuples to be very different, i.e. there are no two tuples that agree in two positions. That is also a simple strategy for producing such codes (the more interesting question is what (x,y) combination is best.)

Think of it this way: assuming you only know part of the tuple. Say the first is unknown: (?, 2, 4) then you want to be able still conclude the correct triple.

https://en.wikipedia.org/wiki/Forward_error_correction

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.