MHB Puzzle Game - How Many Combinations - How Long To Solve

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The discussion revolves around calculating the number of combinations for the puzzle game MillionPuzzleGame.com. Participants share their methods for determining the total combinations and compare results. There is also an inquiry into the time a computer would require to solve the puzzle based on the number of combinations. Various estimates and calculations are presented to assess the complexity of the puzzle. The conversation highlights the mathematical challenges involved in solving the game efficiently.
benjimon
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For this puzzle game:
MillionPuzzleGame.com

I'd like to check I worked out the number of combinations correctly.

Also, how long would a computer take to solve it?
 
Mathematics news on Phys.org
What number of combinations did you get?
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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