A conversation about mathematics inspired by a hat. Presented by Katie Steckles and Peter Rowlett.
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Mathematical Objects: A hat
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#thatlogicproblem round-up
C: $K_A m; \\ K_B d.$
A: $\neg K_A d; \\ m \vDash \neg K_B m.$
B: $d \not\vDash K_B m; \\ (K_A(\neg K_B m)) \vDash K_B (m,d).$
A: $m \wedge K_B(m,d) \vDash K_A (m,d).$
Albert, Bernard and Cheryl have had a busy week. They’re the stars of #thatlogicproblem, a question from a Singapore maths test that was posted to Facebook by a TV presenter and quickly sent the internet deduction-crazy.
First of all: no, it’s not meant to be answered by an average Singaporean student. It’s a hard question from a schools Olympiad test.
Puzzlebomb – November 2013
Puzzlebomb is a monthly puzzle compendium. Issue 23 of Puzzlebomb, for November 2013, can be found here:
Puzzlebomb – Issue 23 – November 2013
The solutions to Issue 23 can be found here:
Puzzlebomb – Issue 23 – November 2013 – Solutions
Previous issues of Puzzlebomb, and their solutions, can be found here.
Games to entertain a commutative mathematician.
I get the Tyne & Wear Metro in and out of work every day. When I don’t have a quality periodical to peruse, I like to play games on my phone. I’ve found a few really good games for my phone that also exercise my maths muscle recently, so I thought I’d write a post about them to share the fun, and prompt you to recommend even more.
Since I’ve got an Android phone, I’m no doubt missing some fantastic games on iOS, but lots of apps these days have versions for both big platforms. I’m also giving UK prices; prices in your country are likely the same numbers with different symbols in front.
Another black and white hats puzzle
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.