, a 14 year-old 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.

[* is the keyboard symbol for a multiplication sign]

1. We find the prime factors of five hundred and ninety-five:
595 = 5 * 7 * 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'*'granid' golden goblets.

If we look back to from step 2 we discover that:
volume of the jar=volume of 'ozvik'*'granid' golden goblets

4. We can work out that 1 golden goblet holds enough oil to fill 'vaswik' crystal spoons: ,br> volume of 1 golden goblet = volume of 'vaswik' crystal spoons

So this means that,
the volume of 'ozvik'*'granid' golden goblets=volume of 'vaswik'*'ozvik'*'granid' crystal spoons

Using the information from step 3 we can figure out that,
the volume of the jar=volume of 'vaswik'*'ozvik'*'granid' crystal spoons.

5. We also know something else important, the oil in the jar lasted for 595 days.
The oil in vaswik'*'ozvik'*'granid' spoons lasted for 595 days

If we look back at the information in step 4 we can discover that,
vaswik'*'ozvik'*'granid' = 595
vaswik'*'ozvik'*'granid' = 5 * 7 * 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 , aged 13, 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.