Prove (constructively) that there is a winning strategy for the first player on any n by n board of Gumdrop. If you don't remember the rules of Gumdrop from class, you can refer to the hwl chocolate problem on Blackboard. Hint: The first move is (2, 2). The Chocolate Problem In the game of "Gumdrop", there are n. m gumdrops arranged in an n by m rectangular grid, where n and m are integers > 2. Two players alternate turns, on each turn eating at least one gumdrop. On your turn, you choose a gumdrop of your choice on the grid, at coordinates i, j. You then eat all gumdrops on the grid at coordinates x, y, where x > i and y > j. That is, you eat all gumdrops in the rectangle whose bottom-left coordinates are i, j. The gumdrop at x = 1, y = 1 (the bottom-left gumdrop) is red, and all other gumdrops are green. If you're particularly greedy, you could choose x = 1, y = 1, and eat all the gumdrops. But that would be a bad idea, because whomever eats the red gumdrop loses the game. As you have to eat at least one gumdrop on your turn, you lose if the red gumdrop is the only one left. a) It turns out that whichever player goes first will win if she plays perfectly. Prove it. b) "Gumdrop" is an unsolved game (like Chess, and unlike Tic-Tac-Toe), meaning that no one has figured out the optimal strategy. Explain why this fact does not contradict your answer to part (a).
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Business, 22.06.2019 11:10
The prebisch–singer hypothesis concludes that: a. technology lowers the cost of manufactured products, so developing countries should see an increase in their terms of trade. b. developing countries experience a long-run decline in their terms of trade, as the demand for primary products in higher-income countries declines relative to their demand for manufactured goods. c. because of unfair trading practices, labor in developing countries is exploited. d. opec has been responsible for a slowdown in the world's standard of living.
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Business, 22.06.2019 13:50
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Business, 22.06.2019 17:50
Which of the following statements is true of unsought products? as compared to convenience products, unsought products are purchased more frequently. unsought products are consumer products and services that customers usually buy frequently, immediately, and with minimal comparison and buying effort. a life insurance policy is an example of an unsought product. unsought products have strong brand identification for which a significant group of buyers is willing to make a special purchase effort. unsought products are those products purchased for further processing or for use in conducting a business.
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Business, 22.06.2019 19:20
After jeff bezos read about how the internet was growing by 2,000 percent a month, he set out to use the internet as a new distribution channel and founded amazon, which is now the world's largest online retailer. this is clearly an example of a(n)a. firm that uses closed innovation. b. entrepreneur who commercialized invention into an innovation. c. business that entered the industry during its maturity stage. d. exception to the long tail business model
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Prove (constructively) that there is a winning strategy for the first player on any n by n board of...
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