This is part one !!! Pls i need help with problems 1, 2 and 3.... thank u! 1. St
ID: 106805 • Letter: T
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This is part one !!! Pls i need help with problems 1, 2 and 3.... thank u!
1. Strategies adopted in favour of Player B:
_An infinite list of both odd and even numbers has been provided. Therefore there is a wide range of numbers to choose from, in order to find out the number.
_An odd number when chosen, is subtracted from the previous determined number, whereas an even number is added with it. Therefore this strategy is helpful for narrowing down the range, i.e finding out the upper limit and lower limit within which the number must lie.
_The numbers from the list can be chosen in any order, therefore there is a chance to determine the narrowest range containing the upper limit and the lower limit quite quickly, if chosen wisely.
_A total of 20 numbers can be chosen, or there are 20 chances to find the number nearest to the number as selected by Player A. Hence the probability of finding out the exact number, or the number correct upto some places of rhe decimal is quite high.
_When 20 chances are over, Player B will be given a chance to guess the number without using the calculator. Depending on how narrow a range he/she had obtained, Player B has a chance to at least, tell the exact number selected by Player A.
2. Strategies adopted against Player B:
_The numbers in both the even and odd lists constitute of only inverses of even and odd numbers, respectively. In the odd list there was a scope to provide fractions with other numbers than 1, to function as numerator. This could have helped Player B find out the exact number more easily, quickly, and accurately.
_No number from either list can be used more than once. Therefore, once a narrow range has been obtained, there would be some difficulty to fine tune the selected number accurately to all places of the decimal, even if Player B has got an idea of the exact estimate of the number.
_Since no number from the lists can be repeated, 20 chances of finding out the selected number correct upto all the 8 decimal places is much difficult.
3. Even if the game was to continue indefinitely, there is a greater chance that the number as chosen by Player A cannot be chosen correct upto all the decimal places. This is because, since no fraction from either list can be used more than once, the scenario could be such that, the number which when added, or subtracted could have given the exact answer, has already been used up before. Although the numbers can be chosen in any order, the fact that odd numbers are subtracted, while even numbers are added, will make it difficult to reach the exact number correct upto all decimal places. Even if a close range of fractions are added or subtracted strategically, there will always be some deviation.
4. A successive combination of "too high, too low" can very effectively help to find out the upper bound or, how far off Player B is. In fact, it will actually help to fine-tune the range in the beginning, thereby reaching the number closest to the number as selected by Player A.
Decimal of fortune follows is a description of a game for two people, Player A and Player B. The object game is for Player B to determine number that has been selected May based on how close Player B has come to Player A's number at the end of the game. Play requires a calculator. with eight decimal places. This decimal must Player A writes down decimal Player B enters thevalue zero into the calculator. Player be between zero and one. B will begin play by selecting a number from E (evens) or List o the number is dosen from List E, it is added to the value in the calculator If the number is selected from List o, it is subtracted from the value in the List is the 1/2n, List E is the infinite list of numbers: 1/2, 1/4, 1/6, 1/8 Player A then tells Player B 1/(2n-1) infinite list of numbers: 1, 1/3, 1/5, whether or not the value in the caleulator is greater than Player A's selected number selected number. If less than Player A's selected number, or equal to Player A's is equal to Player A's number, play terminates. If not, the value in the calculator Player B selects another number that has not been selected before, from either List E or List o and adds it to the value in the calculator if it is from List Eor subtracts if it is from List o in an effort to get closer to t from the value in the calculator Player A's number. Play continues until Player B determines Player A's number or until Player B has chosen 20 numbers from the lists. (Player B may not use any number from the lists more than once, but may choose numbers in any order.) In the latter case, Player B may make a final guess (without further calculations on calculator) the Player B's score is 20 points if Player A's number is determined exactly; otherwise it is n points if the value guessed matches m decimal digits exactly, Notes: Player B needs to keep track of those numbers that have been used. It is are used while play is in progress. It suggested that numbers be written down as they is also suggested that values in the calculator be written down (or stored in memory) they appear, so that if a mistake is made entering a number the previous value may be recovered. ple, a sample game where Player A chooses 0.42000000 (unknown to Player B) is given on the next page. Play this game four times, with each partner assuming the role of Player A twice. Then answer the following questions. 1. What strategies were developed for Player B as the games were played? 2. What strategies were developed by Player A to prevent Pla yer B from deter. mining Player A's number? 3. If the game were to continue "indefinitely," do you think that Player A's number could be determined exactly? Why hy not? Copyright 1994 John Wiley & Sons, Inc.
Explanation / Answer
The strategy that Player B used that Player B enters the value zero in the calculator.Player B we will begin the selecting a number from list E (even) or list(o) if the number is chosen from list E it is added into the value of calculator. If the Number is odd it is subtracted from the value of calculator. Therefore it works in his favor by selecting the number 0. Since if it is even the list will be infinite 1, ½,1/4 and If not that means odd it will be an infinite list of 1,1/3,1/5 etc. An infinite list of both odd and even numbers has been provided. Therefore there is a wide range of numbers to choose from, in order to find out the number. An odd number when chosen is subtracted from the previously determined number, whereas an even number is added to it. Therefore this strategy is helpful for narrowing down the range, i.e finding out the upper limit and lower limit within which the number must lie.The numbers from the list can be chosen in any order, therefore there is a chance to determine the narrowest range containing the upper limit and the lower limit quite quickly if chosen wisely.A total of 20 numbers can be chosen, or there are 20 chances to find the number nearest to the number as selected by Player A. Hence the probability of finding out the exact number, or the number correct to some places of the decimal is quite high.When 20 chances are over, Player B will be given a chance to guess the number without using the calculator. Depending on how narrow a range he/she had obtained, Player B has a chance to at least, tell the exact number selected by Player A.
Answer- 1 No number from either list can be used more than once. Therefore, once a narrow range has been obtained, there would be some difficulty to fine tune the selected number accurately to all places of the decimal, even if Player B has got an idea of the exact estimate of the number. Since no number from the lists can be repeated, 20 chances of finding out the selected number correct up to all the 8 decimal places are much difficult.
Answer -2 No number from either list can not be determined by the player B. Even if the game was to continue indefinitely, there is a greater chance that the number as chosen by Player A cannot be chosen correctly up to all the decimal places. This is because, since no fraction from either list can be used more than once, the scenario could be such that, the number which when added or subtracted could have given the exact answer, has already been used up before. Although the numbers can be chosen in any order, the fact that odd numbers are subtracted, while even numbers are added, will make it difficult to reach the exact number correct to all decimal places. Even if a close range of fractions is added or subtracted strategically, there will always be some deviation.
Answer 3 - A successive combination of "too high, too low" can very effectively help to find out the upper bound or, how far off Player B is. In fact, it will actually help to fine-tune the range, in the beginning, thereby reaching the number closest to the number as selected by Player A.
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