Matt Parker (@standupmaths on Twitter) has tweeted the following Maths Puzzle, to wake you up:
No spoilers in the comments! Send your replies to Matt on Twitter.
Puzzlebomb is a monthly puzzle compendium. Issue 5 of Puzzlebomb, for May 2012, can be found here:
Puzzlebomb – Issue 5 – May 2012
The solutions to Issue 5 can be found here:
Puzzlebomb – Issue 5 – May 2012 – Solutions
Previous issues of Puzzlebomb, and their solutions, can be found here.
Matt’s latest set of puzzles, as part of the Make Britain Count campaign, are online at The Telegraph. This round of puzzles is all about factors, and there have been previous puzzle sets about consecutive numbers and prime numbers.
One would be hard put to ﬁnd a set of whole numbers with a more fascinating history and more elegant properties surrounded by greater depths of mystery — and more totally useless — than the perfect numbers.
— Martin Gardner
There are countless ways to classify integers. Happy, perfect, friendly, sociable, abundant, extravagant, cute, interesting, frugal, deficient, hungry, undulating, weird, vampire… the list goes on. But how useful are such classifications, beyond their inherent interestingness, and as a hook to get people into number theory?
A classic maths puzzle involves a line of one hundred prisoners, who have each been given a black or white hat by their nefarious captor, and must each correctly shout out the colour of their hat to win freedom. The twist is that the prisoners don’t know the colour of their own hat, and though they can see the colours of the hats in front of them, they don’t know many of each colour there are overall. They can confer on a strategy beforehand, and the aim is to get as many of them to correctly identify their hat colour as possible. You can find a full explanation here (and in many other places!)
There are several ‘sequels’ to this puzzle, some involving an infinite number of prisoners and requiring the axiom of choice to solve. This post is about a nice variation on the theme that I heard about at a recent MathsJam. It can (just about) be solved without knowledge of higher mathematics, and though it seems impossible at first glance, the prisoners in this situation can in fact save themselves with 100% certainty.