document.write( "Question 900671: i have to arrange 56 people in groups of 7, and these groups need to change as many times as possible, but no 2 people can be in the same group more than once. how many times can this happen, and what is an ordered way to have them switch? \n" ); document.write( "
Algebra.Com's Answer #546500 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let the 56 people be numbered 1-56\r\n" );
document.write( "Let the 8 groups be numbered 1-8 \r\n" );
document.write( "Each group will consist of the 7 people \r\n" );
document.write( "in the vertical columns \r\n" );
document.write( "\r\n" );
document.write( "group    1  2  3  4  5  6  7  8\r\n" );
document.write( "-------------------------------\r\n" );
document.write( "person   1  2  3  4  5  6  7  8\r\n" );
document.write( "person   9 10 11 12 13 14 15 16\r\n" );
document.write( "person  17 28 19 20 21 22 23 24\r\n" );
document.write( "person  25 26 27 28 29 30 31 32\r\n" );
document.write( "person  33 34 35 36 37 38 39 40\r\n" );
document.write( "person  41 42 43 44 45 46 47 48\r\n" );
document.write( "person  49 50 51 52 53 54 55 56\r\n" );
document.write( "\r\n" );
document.write( "To form the first change slide the people over like this,\r\n" );
document.write( "for instance, person 9 moves from group to group 2\r\n" );
document.write( "\r\n" );
document.write( "group    1  2  3  4  5  6  7  8\r\n" );
document.write( "-------------------------------\r\n" );
document.write( "person   1  2  3  4  5  6  7  8\r\n" );
document.write( "person      9 10 11 12 13 14 15 16\r\n" );
document.write( "person        17 28 19 20 21 22 23 24\r\n" );
document.write( "person           25 26 27 28 29 30 31 32\r\n" );
document.write( "person              33 34 35 36 37 38 39 40\r\n" );
document.write( "person                 41 42 43 44 45 46 47 48\r\n" );
document.write( "person                    49 50 51 52 53 54 55 56\r\n" );
document.write( "\r\n" );
document.write( "Then take the people who stick out on the right and fill them\r\n" );
document.write( "in the gaps at the first\r\n" );
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document.write( "group    1  2  3  4  5  6  7  8\r\n" );
document.write( "-------------------------------\r\n" );
document.write( "person   1  2  3  4  5  6  7  8\r\n" );
document.write( "person  16  9 10 11 12 13 14 15 \r\n" );
document.write( "person  23 24 17 28 19 20 21 22 \r\n" );
document.write( "person  30 31 32 25 26 27 28 29\r\n" );
document.write( "person  37 38 39 40 33 34 35 36\r\n" );
document.write( "person  44 45 46 47 48 41 42 43 \r\n" );
document.write( "person  51 52 53 54 55 56 49 50\r\n" );
document.write( "\r\n" );
document.write( "For the 2nd change, do it again, and \r\n" );
document.write( "person 9 will now move to group 3.\r\n" );
document.write( "\r\n" );
document.write( "group    1  2  3  4  5  6  7  8\r\n" );
document.write( "-------------------------------\r\n" );
document.write( "person   1  2  3  4  5  6  7  8\r\n" );
document.write( "person     16  9 10 11 12 13 14 15 \r\n" );
document.write( "person        23 34 17 28 19 20 21 22 \r\n" );
document.write( "person           30 31 32 25 26 27 28 29\r\n" );
document.write( "person              37 38 39 40 33 34 35 36\r\n" );
document.write( "person                 44 45 46 47 48 41 42 43 \r\n" );
document.write( "person                    51 52 53 54 55 56 49 50\r\n" );
document.write( "\r\n" );
document.write( "group    1  2  3  4  5  6  7  8\r\n" );
document.write( "-------------------------------\r\n" );
document.write( "person   1  2  3  4  5  6  7  8\r\n" );
document.write( "person  15 16  9 10 11 12 13 14 \r\n" );
document.write( "person  21 22 23 34 17 28 19 20 \r\n" );
document.write( "person  27 28 29 30 31 32 25 26\r\n" );
document.write( "person  33 34 35 36 37 38 39 40\r\n" );
document.write( "person  47 48 41 42 43 44 45 46 \r\n" );
document.write( "person  53 54 55 56 49 50 51 52\r\n" );
document.write( "\r\n" );
document.write( "This can continue until person 9 moves to group 8.\r\n" );
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document.write( "Counting the first time, person 9 can appear once in\r\n" );
document.write( "each group, so that 8 times, 7 changes.\r\n" );
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document.write( "Edwin
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