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.

I will be visiting my grandchildren over the next few days and so blogging will be light or non-existent until early next week.

At some point yesterday, this blog reached 10 million page views.

Thanks to everyone for reading and commenting.

Via.

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.

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.

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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England will play New Zealand on Saturday while Wales will play South Africa on Sunday. Of the four quarterfinals matches played last weekend, three were blowouts, with England, New Zealand, and South Africa easily defeating Australia, Ireland, and Japan respectively by margins of over 20 points.

The one nail-biter was between Wales and France where France was ahead for almost the entire game and had a 19-10 lead at the 30-minute mark before Wales fought back and ultimately won 20-19, the last try scored just about seven minutes before the end of the regular 80 minutes of play.

At the 4:00 minute, France missed the conversion of their first try, a kick that players at this level could be expected to make. The ball hit the vertical crossbar and fell back onto the field. The missed two points was the difference between victory and defeat.

English bookmakers are favoring New Zealand to win the championship (5/6), followed by South Africa (10/3), England (9/2), and Wales (10/1).

Here are the highlights of the Wales-France game.