The Genie in the Jar
A genie who lived in a large blue and white porcelain jar served his master by performing miraculous tasks.
Before the genie would carry out a request he asked his master a question that had to be answered correctly.
One day the genie posed this problem:
"This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal spoons. Each day a spoonful was used to perfume the bath of a beautiful princess.
For how many days did the whole jar last?"
The genie's master replied:
"Five hundred and ninety five days."
Immediately this correct answer was given the genie flew off to do his master's bidding.
What three numbers do the genie's words "granid", "ozvik" and "vaswik' stand for?
What is its most obvious factor?
Remember that you are not asked which number is which.
Natasha , a student studying at the Indian Language School, in Lagos, Nigeria sent in her solution to another one of our "much-valued problems", The Genie in the Jar. Thank you Natasha for this very comprehensive explanation of your thinking.
1. We find the prime factors of five hundred
and ninety-five:
$595 = 5\times 7\times 17$, which are the prime factors.
2. We know that the jar holds enough oil to
fill 'granid' silver bottles:
volume of jar = volume of 'granid' bottles
3. If $1$ silver bottle holds enough oil to
fill 'ozvik' golden goblets then,
volume of $1$ silver bottle = volume of 'ozvik' golden goblets
Therefore, based on this knowledge, we can make the
statement:
volume of 'granid' silver bottles = volume of 'ozvik'$\times$
'granid' golden goblets.
If we look back to from step 2 we discover that:
volume of the jar = volume of 'ozvik'$\times$ 'granid' golden
goblets
4. We can work out that $1$ golden goblet holds enough oil to fill 'vaswik' crystal spoons: volume of $1$ golden goblet = volume of 'vaswik' crystal spoons
So this means that,
the volume of 'ozvik'$\times$ 'granid' golden goblets = volume of
'vaswik'$\times$ 'ozvik'$\times$ 'granid' crystal spoons
Using the information from step 3 we can figure out that,
the volume of the jar = volume of 'vaswik'$\times$ 'ozvik'$\times$
'granid' crystal spoons.
5. We also know something else important, the
oil in the jar lasted for $595$ days.
The oil in vaswik'$\times$'ozvik'$\times$'granid' spoons lasted for
$595$ days
If we look back at the information in step 4 we can discover
that,
vaswik'$\times$ 'ozvik'$\times$ 'granid' = $595$
vaswik'$\times$ 'ozvik'$\times$ 'granid' = $5\times 7\times 17$
The genie's words: 'granid', ozvik' and 'vaswik' stand for our numbers five, seven and seventeen.
Do you agree with Natasha's thinking and solution? Chris Milliken also worked hard on this problem and had a different strategy from Natasha. Do you see how and why your solution differs too Chris?
Have you solved this problem in a different way? We would like to hear from you.