Challenging Problem Solving
You've just finished the harvest, and have ten apples, ten bananas, ten carrots, ten dates, and ten eggplants. The market in town will perform any of the unidirectional exchanges shown below any number of times in any order so long as you have the necessary goods at the time of each trade.
The market will take from you:
1) apple and banana
2) carrot and date
3) apple and carrot
4) date and eggplant
5) apple and date
6) banana, carrot, eggplant
and give to you:
1) 2 carrots
2) apple and eggplant
3) banana and date
4) 2 apples
5) 3 eggplants
6) 2 dates

Question

Challenging Problem Solving
You've just finished the harvest, and have ten apples, ten bananas, ten carrots, ten dates, and ten eggplants. The market in town will perform any of the unidirectional exchanges shown below any number of times in any order so long as you have the necessary goods at the time of each trade. 
The market will take from you:
1) apple and banana
2) carrot and date
3) apple and carrot
4) date and eggplant
5) apple and date
6) banana, carrot, eggplant
and give to you:
1) 2 carrots
2) apple and eggplant
3) banana and date
4) 2 apples
5) 3 eggplants
6) 2 dates

anonymous · Answer

For each part a-e, what is the largest number of the given item that you could end up with after trading at the market? 
a. apples
b. bananas
c. carrots
d. dates
e. eggplants