Applying constraint programming to minimal lottery designs

TL;DR

This paper introduces a constraint programming approach to determine the smallest lottery designs that guarantee matching at least two balls in any draw of six, for up to 70 balls.

Contribution

It presents a novel constraint-based method for calculating minimal lottery ticket designs with specific matching guarantees.

Findings

Identified the minimum number of tickets needed for various ball counts.

Demonstrated the effectiveness of constraint programming in lottery design.

Provided computational results for up to 70 balls.

Abstract

We develop and deploy a set of constraints for the purpose of calculating minimal sizes of lottery designs. Specifically, we find the minimum number of tickets of size six which are needed to match at least two balls on any draw of size six, whenever there are at most 70 balls.