Puzzle 82 | Different Pairings

Joey has to arrange 2N sandwiches which are wrapped by different color wrapper in N pairs such that he can feed his N girlfriends (A hypothetical situation it is where we have to ignore the fact “JOEY DOESN’T SHARE FOOD ”). He has to serve them for 2N-1 Days. Girls don’t like repeated pair of color wrapper of their sandwiches.
Design an algorithm for joey so that for 2N-1 days no pair would be same.

Hint: One can solve problem by using 2*N table.

Here is one of the way to generate 2N-1 sets of different pairs efficiently. For convenience, number the different color from 1 to 2N and place these numbers in a 2N table. The pairs for the first set are given by the columns of this table. To generate the next 2N −2 sets, rotate—say, clockwise—all the entries except 1 in the last generated table.
Figure shows the example for N = 3. The entry 1 is fixed and all other entries are rotated clockwise.

References:  The algorithm can be thought of as based on the representation change strategy. Both interpretations of the algorithm outlined above were given by Maurice Kraitchik in Mathematical Recreations [Kra53, pp. 226–227].

This puzzle is contributed by Antara Purohit. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

My Personal Notes arrow_drop_up
Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.