Tuesday 28 March 2017

Truth and Taste



The entire  court of the kingdom had gathered for supper. in the Great Hall His Highness, the king himself sat upon his seat at the end of the table, watching as his servants filled the table with one delicious course after the next.
Once the feast was prepared, the court remained with their hands on their knees, awaiting their king to declare the feast started, as noone may dine before his highness. The king grabbed his goblet and brought it to his lips, but before he could take his first sip of wine,
the doors to the hall burst open as if by a strong wind.
"Stop!", the eyes of the court was now focused on the king's spymaster, his shadows dancing by the candles of the chandalier. "Sire, put down that goblet! The wine is poisoned!"
The commotion that followed quickly spread across the Great hall and through the entire palace! The murmur of whispers were drowned out by the guards yelling orders at each other. The king himself gathered with his spymaster to see the master of the cellar. It was worse than he thought.
Out of the one hundred barrels of wine they had received that morning, all had been contaminated with deadly poison!
But it wasn't the ordinary, run of the mill poison that were stored in the barrels, but one of two magical potions. It was either that of Truthium, that when consumed has no immediate effect, but if and only if the next thing the consumer says is a false statement, he or she will immediately fall dead!
The other poison is called Falsium, that when consumed has no immediate effect, but if and only if the next thing the consumer says is a true statement, he or she will immediately fall dead!
Clearly they are dealing with a cunning and subtle assassin.

What a disaster!, the king laments. That shipment was supposed to last for the entire month, but according to the spymaster not a single barrel was free of poison. That the entire court would go sober for the entire month was unthinkable!
Then it occurred to him: what if they simply drank of the wine with the Truthium, and then have the court say something evidently true, such as "our king is a noble and merciful king"! Or from the falsium, and say something they know to be false. The poison, then would be powerless!
Alas, that were not to be, for the spymaster could not tell which barrel contained which poison, or how many of which poison was used. All he knew was that all barrels contained one of the two poisons, but for all he cared the barrels contained only truthium or only falsium.

The king, determined to see his solution realized, wrote a letter to the tasters' guild explaining the situation.
He gave the message to his messenger along with a skin of water and watched him gallop away! He would have his wine even if he had to sacrifice one hundred tasters!
Of course, it might not be necessary to sacrifice that many. It was a well-known fact the guildmaster of the tasters was an educated man proficient in the study of logic. Maybe he could figure out a way to determine what barrel contained which poison with only fifty tasters. Or ten!
After all, there are only ten times ten barrels in the shipment, so it would not surprize the king if it turned out to be a way to solve this problem with only ten tasters at most. And if there were, the guildmaster would undoubtedly figure it out!
And as night fell on the kingdom, the court were forced to drink water to their meal instead of wine. Early in the morning, the king was informed that the tasters that the guildmasters had sent was waiting outside the palace, so the king went out to greet them. As he entered the courtyard, his jaws dropped.
The guildmaster had not sent a hundred tasters, nor fifty, nor ten.
Two tasters were there! Only two!

How did the king manage to determine the content of all those one hundred barrels with only two tasters?

BONUS QUESTION 1: Is it possible to solve this problem with only one taster being sacrificed?
BONUS QUESTION 2: Is it possible to solve this problem with no sacrifices at all?

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