5 hours ago
2
Today’s puzzles celebrate prime numbers – those beguiling numbers that divide only by themselves and 1, a sequence that begins 2, 3, 5, 7, 11, 13, and carries on forever.
The first question was suggested by Steve Thompson…a maths teacher who became one of the UK’s most successful TV screenwriters.
His latest thriller, Prime Target, tells the story of a mathematician whose research into the primes has unexpected consequences (and is played by Leo Woodall, pictured above.)
1. Prime power
Without using a calculator, what is the last digit of 3 to the power of a million, i.e 31,000,000?
The second puzzle is one of my all-time favourites.
2. The 7-Eleven
A shopper walks into a convenience store and buys four items. The cashier says the total is £7.11.
‘How funny,’ says the shopper. ‘That’s the name of the shop.’
‘What’s also funny is that I multiplied the prices of the four items together,’ says the cashier.
‘Aren’t you supposed to add the items together?’ replies the shopper.
‘You can do if you like – the total is exactly the same.’
What are the prices of the items?
I’ll be back at 5pm UK with the solutions. (And I’ll add some hints at noon.)
Thompson had the idea for Prime Target two and a half decades ago when he was head of maths at a grammar school in Kingston-upon-Thames. The science writer Simon Singh presented a talk in his school in which he explained how prime numbers are used in cryptography to make the internet secure.
Prime numbers are considered the building blocks of maths is because every whole number can be expressed as the product of a unique combination of primes. For example, 100 = 2 x 2 x 5 x 5. Or 102 = 2 x 3 x 17.
But prime numbers occur in a way that looks random – and this lack of a pattern can be harnessed to keep data secret. If a pattern is found in the primes, however, these secrets will no longer be secure.
The idea captured Thompson’s imagination: “Here was a quest to find a number pattern that had been going on for thousands of years, and yet here we were in the 21st century, basing all of computer security on the fact that no pattern existed. It made me realise – if someone were finally to discover a pattern, then our whole digital world would be at risk.”
Shortly after Singh’s visit, Thompson quit his job to try his hand writing plays. He then become a celebrated screenwriter, with TV credits including Sherlock and Dr Who. But he never forgot about his prime number idea, and it became Prime Target, which was released on Apple TV+ to positive reviews last month.
Thompson’s contribution above is his favourite puzzle, which features 3, a prime number. You can’t use a calculator for the first puzzle, but you can for the second one. You will need to find the prime divisors of a large number, for which you are allowed to use this site here.
NO SPOILERS. Please discuss your favourite primes.
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
