Thursday 10 August 2017
Sunday 30 July 2017
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?
Tuesday 12 April 2016
Solutions!
I've decided to reveal the answers to my puzzles. I've always felt that by revealing the answer you deprive something from the readers, even if you are only presenting the option of readin the solution. But lately I've come to realize that this is not a reasonable way to go about it.
First of all, I have to prove that there is in fact a solution. Maybe you should take my word for it. Maybe you should just assume I'm trolling you. Or maybe, and this might be the most likely of all, I have made a mistake or expressed myself poorly, and you should be given an opportunity to make your objections.
Second of all, I have to present the option of checking if the answer you have come up with is correct. I try to make it so that you know what the correct answer is when you see it, but if you have taken the time to solve my puzzle you should be granted the satisfaction to know that you are right; and sometimes the answer you thought was so clear to you might not be as clever as it seemed. I'd hate to allow any such derailed conclusions run rampant in the world.
Finally, the solutions of my problems are in fact kind of neat, and even if it's important that you come up with it by yourself, I still want the people who visit my blog to see both the problem and the solution.
So I've added a page where my puzzles and their solutions can be accessed. As I write more solutions they will be added to this page; as will any new puzzles.
First of all, I have to prove that there is in fact a solution. Maybe you should take my word for it. Maybe you should just assume I'm trolling you. Or maybe, and this might be the most likely of all, I have made a mistake or expressed myself poorly, and you should be given an opportunity to make your objections.
Second of all, I have to present the option of checking if the answer you have come up with is correct. I try to make it so that you know what the correct answer is when you see it, but if you have taken the time to solve my puzzle you should be granted the satisfaction to know that you are right; and sometimes the answer you thought was so clear to you might not be as clever as it seemed. I'd hate to allow any such derailed conclusions run rampant in the world.
Finally, the solutions of my problems are in fact kind of neat, and even if it's important that you come up with it by yourself, I still want the people who visit my blog to see both the problem and the solution.
So I've added a page where my puzzles and their solutions can be accessed. As I write more solutions they will be added to this page; as will any new puzzles.
Wednesday 20 January 2016
The Butcher's Balance Scale
Here is my variation on a classic logic puzzle:
A butcher uses a balance scale in order to measure if he gives the right amount of meat to the customers.
For this scale he has six weights, all of which weigh a whole number of grams, for which he can weigh against the meat a maximum of all weights added together. If the scale is balanced he knows the meat weighs the same as the sum of all weights.
Furthermore, if he combines the weights in the right way he can weigh against meat weighing any whole number of grams under the sum of all weights and have the scale balance.
For example, if all the weights combined weighs 17 grams he can still use one or more weights to weigh 1 gram or 2 grams or 3 grams or 4 grams etc. all the way up to 17 grams, but not any more than 17 grams.
Knowing this, what is the most he could possibly weigh with these weights?
A butcher uses a balance scale in order to measure if he gives the right amount of meat to the customers.
For this scale he has six weights, all of which weigh a whole number of grams, for which he can weigh against the meat a maximum of all weights added together. If the scale is balanced he knows the meat weighs the same as the sum of all weights.
Furthermore, if he combines the weights in the right way he can weigh against meat weighing any whole number of grams under the sum of all weights and have the scale balance.
For example, if all the weights combined weighs 17 grams he can still use one or more weights to weigh 1 gram or 2 grams or 3 grams or 4 grams etc. all the way up to 17 grams, but not any more than 17 grams.
Knowing this, what is the most he could possibly weigh with these weights?
Monday 2 November 2015
New number-puzzle!
I really should update more often...
Oh well!
23, 9, 10, 15, 9, ??, 29, 10, 31, 10, 14
Oh well!
23, 9, 10, 15, 9, ??, 29, 10, 31, 10, 14
Thursday 5 February 2015
Another puzzle!
Did you miss me?
Of course you did! How else will you get on with your brain-teasers?
And brain-teasers I've got. I am currently in the process of making another Knights and Knaves style puzzle ( i.e. Wedding Whoopsies ) but there's a lot to keep track on when you do it. Until then here is a small number sequence for you to complete:
15, 175, 671, 1695, 3439, ??
For your information, I don't actually know if this puzzle can be solved. I know a solution that would satisfy the problem, but as far as I know there isn't a way to arrive at the correct solution, or the puzzle might be too ambiguous.
If I were to die, this puzzle would remain unsolved if it turns out to be too difficult for anyone on this planet.
But that probably won't turn out to be the case...
Of course you did! How else will you get on with your brain-teasers?
And brain-teasers I've got. I am currently in the process of making another Knights and Knaves style puzzle ( i.e. Wedding Whoopsies ) but there's a lot to keep track on when you do it. Until then here is a small number sequence for you to complete:
15, 175, 671, 1695, 3439, ??
For your information, I don't actually know if this puzzle can be solved. I know a solution that would satisfy the problem, but as far as I know there isn't a way to arrive at the correct solution, or the puzzle might be too ambiguous.
If I were to die, this puzzle would remain unsolved if it turns out to be too difficult for anyone on this planet.
But that probably won't turn out to be the case...
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