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# The Genie in the Jar

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### Adding All Nine

### Double Digit

### Repeaters

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Age 11 to 14

Challenge Level

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?

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?

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.