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In an infinite lottery can you create a lottery ticket that always wins? This is the idea behind a 50-year-old maths problem that has now been solved.

In a standard lottery, you have a ticket with聽a handful of numbers on it and if they match the randomly selected numbers from the lottery, your ticket wins. Each ticket can have several rows in it giving you several chances to win. This means that a long enough ticket could in principle have every possible winning combination meaning that it always wins 鈥� although it would cost so much money to do this in reality it wouldn鈥檛 be worth it.

But in an infinite lottery things are a little different. The winning collection of numbers is infinitely long, and each ticket can have an infinite number of rows, with each row containing an infinite number of numbers. In this situation, it鈥檚 far less obvious whether it鈥檚 possible to create a ticket that always wins.

David Schrittesser and Asger T枚rnquist at the University of Copenhagen found that the answer is that it isn鈥檛 possible to have a ticket that always wins the infinite lottery 鈥� half a century after mathematician Adrian R.D. Mathias first posed the question.

鈥淣obody took the slightest notice for 30 years, and then suddenly people got interested again. It鈥檚 very satisfying to see,鈥� says Mathias. Around 20 years ago, some mathematicians rediscovered the problem and started to make progress. Eventually聽Schrittesser and T枚rnquist became interested as well, but it took them four years before they cracked it.

The pair used ideas from Ramsey Theory to tackle the problem, a part of mathematics that looks at how order appears in large structure. They found that in an infinite lottery, a sort of structure arises that means the winning numbers clump together, but in a way that means a ticket that always wins just can鈥檛 exist.

鈥淲ith these kinds of problems you don鈥檛 sit down and say I鈥檓 going to be the one who solves it because everyone has tried,鈥� says Schrittesser. 鈥淭here鈥檚 a little bit of serendipity.鈥�