Summary Guaranteeing a Win on the UK National Lottery arxiv.org
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The text discusses mathematical strategies and equations to ensure a victory in the UK National Lottery, encompassing lottery designs, rearrangements, and constraints.
Slides
Slide Presentation (8 slides)
Key Points
- The UK National Lottery involves choosing six numbers between 1 and 59 and six balls being randomly selected from a set of 1 to 59.
- There are mathematical equations and proofs discussed in relation to guaranteeing a win on the UK National Lottery.
- The concept of segregated lottery designs and independent sets is introduced, along with the significance of webbings and toes.
- Prolog code is used to calculate upper and lower bounds for the lottery numbers and solve constraint problems.
- The minimum number of tickets needed to guarantee a win on the UK National Lottery is calculated using a program written in Prolog.
Summaries
23 word summary
This excerpt explores mathematical equations and proofs for guaranteeing a win on the UK National Lottery, including lottery designs, equations, rearrangements, and constraints.
44 word summary
The excerpt discusses mathematical equations and proofs related to guaranteeing a win on the UK National Lottery. It introduces the concept of lottery designs and presents equations and rearrangements to prove a contradiction. The text also discusses the constraints and calculations involved in guaranteeing
464 word summary
In the UK National Lottery, players choose six numbers between 1 and 59. During the draw, six balls are randomly selected without replacement from a set of 1 to 59. A prize is awarded to players who match at least two of
An (n, k, p, t; j)-lottery design is a hypergraph H = (X, B), such that there are n vertices in X, j elements in B, each B contains k vertices, and for any subset
Our strategy is based on a previous paper [BR98], but we have made corrections and simplifications to the statements and proofs. An (n, k, t)-covering design is a k-uniform hypergraph where every subset of size t appears
We can create a new lottery design by replacing a variable in an existing design. This new design has certain properties that allow us to guarantee a win. The results mentioned in the text are similar to those found in previous studies. However, there are some
The excerpt discusses mathematical equations and proofs related to guaranteeing a win on the UK National Lottery. The first part presents equations and rearrangements to prove a contradiction. The next part introduces two lemmas that provide constraints to Prolog. Lemma 4
The excerpt discusses the constraints and calculations involved in guaranteeing a win on the UK National Lottery. It introduces the concept of segregated lottery designs and independent sets, and explains the significance of webbings and toes. The excerpt includes a lemma that provides an
The output from the main predicate provides information about the lottery numbers in a specific range. The program conjectures values for certain cases and checks them manually. It uses various predicates to establish upper and lower bounds, compute possible vectors, and solve constraint problems.
The text discusses the distribution of toes in the UK National Lottery. It presents mathematical calculations and reasoning to determine the number of toes in each block. The author uses Prolog code to generate possibilities and eliminate certain cases. The text concludes that there are
The excerpt discusses the computation of lottery numbers for the UK National Lottery. It presents a Prolog code that calculates the upper bound for the lottery numbers. The code includes functions for determining possible lottery numbers, calculating upper bounds, and finding covering designs. The
The code excerpt is a program written in Prolog that calculates the minimum number of tickets needed to guarantee a win on the UK National Lottery. It includes various predicates and functions for performing calculations and generating exceptions. The main goal is to find the values of
This text excerpt includes various references and author names related to the topic of a constraint solver and the lottery problem. It mentions two specific papers: "An open-ended finite domain constraint solver" by Carlsson, Ottosson, and Carlson, and "