Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some other
possibilities for yourself!
Choose two digits and arrange them to make two double-digit
numbers. Now add your double-digit numbers. Now add your single
digit numbers. Divide your double-digit answer by your single-digit
answer. Try lots of examples. What happens? Can you explain it?
Take any four digit number. Move the first digit to the 'back of
the queue' and move the rest along. Now add your two numbers. What
properties do your answers always have?
1. We find the prime factors of five hundred
$595 = 5\times 7\times 17$, 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
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
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
If we look back at the information in step 4 we can discover
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.