The solution to yesterday’s logic puzzle

The solution to yesterday’s puzzle was deduced by some in the comments. I was not able to solve the puzzle myself but in such cases, once I know the solution, I try to figure out why I could not figure it out, to see what I had overlooked.

In this case there are four possibilities for the two coin tosses: HH, HT, TH, and TT where H stands for heads and T for tails. The two coin tosses are independent of each other and so knowing the result of one doesn’t enable one to predict the result of the other. This tempted me to ignore (or not properly register) the information that each person gets to see the result of his or her own toss before predicting the other. And since the captives each gets to make just one guess, that seemed to me to suggest that they must guess wrong at some point.
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Nice little brain teaser

I came across this nice little puzzle that I got from the Quora website from someone named Alejandro Jenkins who said that he cannot recall where he first heard or read about it. In its essentials it is easy to state and understand even though, as seems to be the tradition with such puzzles, a story is constructed around it.

The two leading mathematicians in the kingdom, Alice and Bob, have run afoul of their tyrannical king. Rather than behead them outright, the king decides to prolong their misery by locking them in separate dungeons, so that any communication between them is impossible.

Each morning, a guard is to enter the corresponding dungeon and toss a coin so that the prisoner in that dungeon can see the outcome. Then the prisoner will be asked to guess the outcome of the coin toss in the other dungeon (i.e., Alice has to guess the outcome of the toss witnessed by Bob, and Bob has to guess the outcome of the toss witnessed by Alice). If at least one of the two prisoners guesses correctly, they will live to see another day. Otherwise they will be put to death forthwith.

It would seem that the mathematicians are doomed. But as they are being led away in chains Alice and Bob manage to confer for a brief moment and they agree on a strategy that will delay their execution indefinitely. What is the strategy?

What I like about this puzzle is that there is no trickery involved, no hidden meanings and the like. It is a straightforward logic puzzle. Jenkins provides the solution but for some reason, I cannot deep link to it and so will wait a day to let people discuss it in the comments if they so choose and then post the solution in the comments.

Isn’t regular football brutal enough?

American football is a brutal game and so it should not be surprising that it occasionally erupts into outright violence. This feature was on display recently when Myles Garrett, a player for the Cleveland Browns, yanked off the helmet of an opposing player and repeatedly beat him on the head with it until he was restrained by other players. As is often the case there were events that led up to this assault but it was still egregious by any standards. In fact, yanking out a player’s helmet can be very dangerous because the neck is violently jerked. He has been suspended indefinitely but it made me wonder at what point this kind of on-field violence moves into a territory where the perpetrator is subject to legal prosecution.
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A critique of commercialized mindfulness

I am sure that pretty much everyone has heard the term ‘mindfulness’ being bandied about in the media. While it has its roots in Buddhist meditative practice, it has been taken to mean that, at least in its most drastically simplified form, it involved ‘living in the moment’, that one should pay full attention to what one is doing at any given time and not be trying to do many things at once. i.e., it is the opposite of multitasking. For example when you are driving, focus on where you are going and how you are driving and don’t try to talk on the phone, text, read or daydream.
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Rugby World Cup: South Africa emerge champions

They defeated England in the final by a comfortable margin of 32-12. Up to the 66th minute of regular time, the points were entirely made up of penalty goals with South Africa leading by 18-12. Then in the last 15 minutes, they scored two tries and converted them to put the game out of England’s reach.

In the other match on Friday, New Zealand easily beat Wales 40-17 to take third place. This game was far more open and attacking than the final.

South Africa beat Wales to go to Rugby World Cup final

By beating Wales 19-16 in a close game, South Africa earns a place in the finals next Saturday where they will play England. New Zealand will play Wales on Friday for third place. The game today, like the other semi-final, was largely a defensive one with just one try scored by each side, the other 21 points coming off seven penalties. While this makes the game less scintillating than attacking rugby where a team passes the ball back and forth across the field in successive phases until a try is scored, defensive games also have their own appeal and you get to see some superb kicking in the try and penalty conversions by both sides.

Since both England and South Africa won largely with their defenses, that may portend a defensive game for the final too. But whatever style of play emerges, it is expected to be a close game.

Here are the highlights.

World Cup rugby upset

England beat New Zealand, the winners of the previous two World Cups in 2011 and 2015, in a stunning upset in the current World Cup, winning 19-7 in a defensive, forwards-dominated game, with each side scoring only one try, all the other points coming from penalties. New Zealand had beaten England in 15 of their last 16 exchanges.

I wrote before of the pre-game haka ritual of the New Zealand team, part of the psychological battle, and there were plenty of interesting comments to that post discussing the meaning and purpose of the haka and how teams respond to it. Apparently, the English team had decided on a different way to respond.
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