Buying and Selling Game Contest 15 Results

What is the Buying and Selling Game?

For the benefit of those who have not entered this contest, here is a brief explanation of how the game works.

Participants are required to buy goods with an allocated amount of money. They are given a choice of 6 goods and all these goods are available in any of the 5 towns, cities, islands or planets in the game. The buying prices of all goods are provided in the question.

The participants are then required to sell all of their goods on a future date. The selling prices for all goods in all towns, cities, islands or planets are not provided. Instead, the question provides a triangle distribution for the selling price of each good in each town, city, island or planet. For the triangle distribution, the minimum, maximum, and mode values are provided.

The participant that has the most money after selling all his or her goods is the winner.

Responses to the contest are made in the comments section of the post. If several participants make the same amount of money, the person who entered (commented) first will win. The format of the required entry is explained in detail in the contest itself.

For a more detailed explanation, you can access the contest post using the following link.

Results of the contest

Table 1 contains the selling prices generated by the ‘Buying and Selling’ Game model for each item of office equipment from each town or city.

Table 1: Selling prices of all items of office equipment for each town and city

Table 2 contains responses and the profit made by each participant.

Table 2: Participant responses and profit

Congratulations to @crrdlx for winning Contest 15 of the 'Buying and Selling’ Game.

In Stock Town, he bought 333 filing cabinets at $60 each. He paid total of $19,980

In Corp Town, he sold the 333 filing cabinets at $84.30 each. He received a total of $28,072. Therefore, he made a profit of $8,092 (28,072 – 19,980).

Highest possible profit

The strategy that would have generated the highest profit would have been to buy 66 desks from Cryto City at $300 each and then selling them at Corp Town for $559.94 (as generated by the model). This would have generated a profit of $17,156.

Table 3 contains the lowest buying prices, the highest selling prices and the highest profit for selling each item of office equipment.

Table 3: Lowest buying price and highest selling price

I would also like to thank @sifondeseltz, @jizzyjoe, @sinahit, @razielmorales, and @jeffersom for participating.

Tips for future games

To achieve the best chance of winning the game (i.e. earning the highest profit). Participants need to make the best use of the information they are given. The participant should buy from the place that sells the good at the lowest price and sell at the place that will offer the highest price.

To inform the decision further, participants should also consider the mean and median prices for each good in each place. The mean and median for a triangle distribution can be calculated using the following formulae.

Mean = (Minimum + Maximum + Mode)/3

Median when Mode ≥ (maximum – minimum)/2 (i.e. mode closer to maximum)
Minimum + (((maximum – minimum) × (mode – minimum))/2)^0.5

Median when Mode ≤ (maximum – minimum)/2 (i.e. mode closer to minimum)
Maximum - (((maximum – minimum) × (maximum – mode))/2)^0.5

Proof Median

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