Strategic Transfer in Logical Abilities in Children Playing Mastermind and an Analogue

Strategy development and the use of strategy as a mechanism of transfer was examined in sixty elementary students while playing the logical deduction game Mastermind and a familiar analogue. In the first couple of two-way ANOVAs subjects showed that they are in fact learning or developing a task-specific strategy that can be applied across the two types of games regardless of which game was in the target position of a transfer paradigm. This suggests that subjects were able to focus on structural similarities rather than surface features and apply what was learned between the game isomorphs. Both the third and fourth ANOVAs indicate that strategic transfer did occur between the Family Dinner Table game and Mastermind game, when mastermind was in the target position of a transfer paradigm. This suggests that strategies can be used as a mechanism in transfer

Strategic Transfer in Logical Abilities in Children Playing Mastermind and an Analogue

Strategy development and the use of strategy as a mechanism of transfer was examined in sixty elementary students while playing the logical deduction game Mastermind and a familiar analogue. In the first couple of two-way ANOVAs subjects showed that they are in fact learning or developing a task-specific strategy that can be applied across the two types of games regardless of which game was in the target position of a transfer paradigm. This suggests that subjects were able to focus on structural similarities rather than surface features and apply what was learned between the game isomorphs. Both the third and fourth ANOVAs indicate that strategic transfer did occur between the Family Dinner Table game and Mastermind game, when mastermind was in the target position of a transfer paradigm. This suggests that strategies can be used as a mechanism in transfer

Improved Approximation Algorithm for the Number of Queries Necessary to Identify a Permutation

In the past three decades, deductive games have become interesting from the algorithmic point of view. Deductive games are two players zero sum games of imperfect information. The first player, called "codemaker", chooses a secret code and the second player, called "codebreaker", tries to break the secret code by making as few guesses as possible, exploiting information that is given by the codemaker after each guess. A well known deductive game is the famous Mastermind game. In this paper, we consider the so called Black-Peg variant of Mastermind, where the only information concerning a guess is the number of positions in which the guess coincides with the secret code. More precisely, we deal with a special version of the Black-Peg game with n holes and k >= n colors where no repetition of colors is allowed. We present a strategy that identifies the secret code in O(n log n) queries. Our algorithm improves the previous result of Ker-I Ko and Shia-Chung Teng (1985) by almost a factor of 2 for the case k = n. To our knowledge there is no previous work dealing with the case k > n. Keywords: Mastermind; combinatorial problems; permutations; algorithm

The Query Complexity of Mastermind with l_p Distances

Consider a variant of the Mastermind game in which queries are l_p distances, rather than the usual Hamming distance. That is, a codemaker chooses a hidden vector y in {-k,-k+1,...,k-1,k}^n and answers to queries of the form ||y-x||_p where x in {-k,-k+1,...,k-1,k}^n. The goal is to minimize the number of queries made in order to correctly guess y. In this work, we show an upper bound of O(min{n,(n log k)/(log n)}) queries for any real 10. Thus, essentially any approximation of this problem is as hard as finding the hidden vector exactly, up to constant factors. Finally, we show that for the noisy version of the problem, i.e., the setting when the codemaker answers queries with any q = (1 +/- epsilon)||y-x||_p, there is no query efficient algorithm

Strategic Transfer in Logical Abilities in Children Playing Mastermind and an Analogue

Strategy development and the use of strategy as a mechanism of transfer was examined in sixty elementary students while playing the logical deduction game Mastermind and a familiar analogue. In the first couple of two-way ANOVAs subjects showed that they are in fact learning or developing a task-specific strategy that can be applied across the two types of games regardless of which game was in the target position of a transfer paradigm. This suggests that subjects were able to focus on structural similarities rather than surface features and apply what was learned between the game isomorphs. Both the third and fourth ANOVAs indicate that strategic transfer did occur between the Family Dinner Table game and Mastermind game, when mastermind was in the target position of a transfer paradigm. This suggests that strategies can be used as a mechanism in transfer