The Genie in the Jar

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.