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World Cup squads and the Birthday Paradox

World Cup squads and the Birthday Paradox
By Mark Mason on 16-05-18 10:28. Comments (0)
England's squad for the 2018 World Cup is being announced today. 23 players will make the trip to Russia - and coincidentally 23 is also the number at which the chance of two people sharing a birthday reaches 50 per cent. In fact it's a shade over: 50.73 per cent. Yes, you read that right - with just 23 people gathered together, it's more likely than not that two of them will have the same birthday.

The incredible ‘Birthday Problem'

The incredible ‘Birthday Problem'
By Mark Mason on 12-10-12 14:01. Comments (0)
How many people do you have to gather together in a room before it becomes more likely than not that at least two of them will share a birthday? This teaser is something I mention on the Central Line walk (which passes the wonderful Gresham College, where I first learned about it.) For years I've struggled to convince people that the answer - just 23 - is correct. But recently I found a way of doing it that really brings the truth of the puzzle home ...

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Rubik's Cube

A Rubik’s cube has more combinations than light travels inches in a century. This is my favourite illustration of how a very small number of factors can produce an absurdly complicated situation. A silly little toy, with only three squares in each of its three dimensions. How can that get complicated? Well, as anyone who's ever tried to solve one just by guessing will tell you, it gets very complicated. The number of possible combinations is 43,252,003,274,489,856,000. Forget billions - that's 43 quintillion and change. (In fact the cube's manufacturers just said ‘billions' in their advertising, figuring that no one would know what a quintillion was. It's a billion billion.) The number of inches light travels in a century, meanwhile, is a mere 37,165,049,856,000,000,000. Or thereabouts.