Question 9
In a video game, you start the game with 10 gold coins, 10 wooden coins, 10 stone coins, 0 silver coins and 0 diamond coins.
There are four trading options that are available:
a.) Trading gold coin(s) to a silver coin:
The cost increases by 1 gold coin each time you do a trade.
- First trade: exchange 1 gold coin → receive 1 silver coin.
- Second trade: exchange 2 gold coins → receive 1 silver coin.
- Third trade: exchange 3 gold coins → receive 1 silver coin, and so on.
b.) Trading wooden coin(s) to silver coins:
The cost increases by 1 wooden coin each time you do a trade.
- First trade: exchange 3 wooden coins → receive 2 silver coins.
- Second trade: exchange 4 wooden coins → receive 2 silver coins.
- Third trade: exchange 5 wooden coins → receive 2 silver coins, and so on.
c.) Trading stone coins(s) to a diamond coin:
The cost increases by 1 stone each time you do a trade.
- First trade: exchange 2 stone coins → receive 1 diamond coin.
- Second trade: exchange 3 stone coins → receive 1 diamond coin.
- Third trade: exchange 4 stone coins → receive 1 diamond coin, and so on.
d.) Trading a silver coin to a diamond coin:
Fixed rate: exchange 1 silver coin → receive 1 diamond coin.
Some additional trading conditions:
- You may perform trades in any order and any number of times, provided you have enough coins at the moment of the trade.
- If you do not have enough coins to perform the required condition for a trade, then you cannot perform that trade. (You cannot partially perform a trade).
- The counters for each of the different trade types are independent with each other.
What is the maximum number of diamond coins you can obtain? Give a full and detailed explanation and describe the general strategy that achieves the maximum.
Please write down your full solution at the reverse side of this sheet.
There are four trading options that are available:
a.) Trading gold coin(s) to a silver coin:
The cost increases by 1 gold coin each time you do a trade.
- First trade: exchange 1 gold coin → receive 1 silver coin.
- Second trade: exchange 2 gold coins → receive 1 silver coin.
- Third trade: exchange 3 gold coins → receive 1 silver coin, and so on.
b.) Trading wooden coin(s) to silver coins:
The cost increases by 1 wooden coin each time you do a trade.
- First trade: exchange 3 wooden coins → receive 2 silver coins.
- Second trade: exchange 4 wooden coins → receive 2 silver coins.
- Third trade: exchange 5 wooden coins → receive 2 silver coins, and so on.
c.) Trading stone coins(s) to a diamond coin:
The cost increases by 1 stone each time you do a trade.
- First trade: exchange 2 stone coins → receive 1 diamond coin.
- Second trade: exchange 3 stone coins → receive 1 diamond coin.
- Third trade: exchange 4 stone coins → receive 1 diamond coin, and so on.
d.) Trading a silver coin to a diamond coin:
Fixed rate: exchange 1 silver coin → receive 1 diamond coin.
Some additional trading conditions:
- You may perform trades in any order and any number of times, provided you have enough coins at the moment of the trade.
- If you do not have enough coins to perform the required condition for a trade, then you cannot perform that trade. (You cannot partially perform a trade).
- The counters for each of the different trade types are independent with each other.
What is the maximum number of diamond coins you can obtain? Give a full and detailed explanation and describe the general strategy that achieves the maximum.
Please write down your full solution at the reverse side of this sheet.