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Good job ajttja and Gil-Gandel! And I'm glad you guys got the same thing as me. Pretty good for a 14-year-old?
Yes, not really a riddle but a genuine piece of math.
An apothecary has a set of balance scales and the following weights: 1g, 3g, 9g and 27g. How many different weights can he weigh (clumsy sentence but I'm short of synonyms) with this equipment?
i don't understand the question but i know there some reason the you have the weights being 3 to the 0, 3 to the first, 3squared, and 3cubed so i get some credit.
In Gil-Gandel's problem the answer is any integer up to 40g. If it balances with the 1g, it is one gram. If it balances on the same side as the 1g while opposite the 3g, it is 2g. 3 and 4 are obvious, 5 balances 9 on one side with the 1 and 3 on the other. This can be followed for any number up to 40. For example, if the weight is 32g, it will balance with 27g and 9g on the opposite side, and 3g and 1g on the same side
the sign said H p z u u l q l
Nothing - signs can't talk.
Yes, and you can extend this indefinitely with powers of 3 (as ajttja realized).
I repeat the correct answer: he can weigh 40 different weights. :-)
06-jwagg and ajttja gave the good explanations, though the wrong answers.
It means the sign maker is an alcoholic and the person who bought the sign will be searching for someone else to do it in the future.
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