## 17 Apr 2013

### The Currency of Tripolina: Middle Secondary Mathematics Competition Question

The island of Tripolina has a strange currency. The tryad is denominated in powers of 3; they have coins worth 1, 3, 9, 27 and 81 tryads. Alice is walking around the local market and feels that her purse is really far too heavy. Back at the hotel she had counted out all her coins and found that she had five each of 1, 3, 9 and 27 tryads. At the market, she spotted an ornate vase that would make a lovely present for her mother. The vase cost 59 tryads. What is the maximum number of coins that Alice can use to pay for the vase without receiving any change?

Pleased with her purchase, Alice heads for a coffee shop. A coffee costs 5 tryads. Alice frowns when the change arrives and asks for the minimum number of coins. Which coin did Alice pay with? And what is the minimum number of coins she can receive in change?

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