Make an 8x8 grid of numbers 1-64, each number representing
one of the 64 people.
I'll connect the 8 members in each group with lines.
The first 8 groups will consist of the 8 rows:
1---2---3---4---5---6---7---8
9--10--11--12--13--14--15--16
17--18--19--20--21--22--23--24
25--26--27--28--29--30--31--32
33--34--35--36--37--38--39--40
41--42--43--44--45--46--47--48
49--50--51--52--53--54--55--56
57--58--59--60--61--62--63--64
The second 8 groups will consist of the 8 columns:
1 2 3 4 5 6 7 8
| | | | | | | |
9 10 11 12 13 14 15 16
| | | | | | | |
17 18 19 20 21 22 23 24
| | | | | | | |
25 26 27 28 29 30 31 32
| | | | | | | |
33 34 35 36 37 38 39 40
| | | | | | | |
41 42 43 44 45 46 47 48
| | | | | | | |
49 50 51 52 53 54 55 56
| | | | | | | |
57 58 59 60 61 62 63 64
To make the third 8 groups, make the grid again on the
right as below. Then take the 8 diagonals as the 8 groups.
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
\ \ \ \ \ \ \ \
9 10 11 12 13 14 15 16 9 10 11 12 13 14 15 16
\ \ \ \ \ \ \ \
17 18 19 20 21 22 23 24 17 18 19 20 21 22 23 24
\ \ \ \ \ \ \ \
25 26 27 28 29 30 31 32 25 26 27 28 29 30 31 32
\ \ \ \ \ \ \ \
33 34 35 36 37 38 39 40 33 34 35 36 37 38 39 40
\ \ \ \ \ \ \ \
41 42 43 44 45 46 47 48 41 42 43 44 45 46 47 48
\ \ \ \ \ \ \ \
49 50 51 52 53 54 55 56 49 50 51 52 53 54 55 56
\ \ \ \ \ \ \ \
57 58 59 60 61 62 63 64 57 58 59 60 61 62 63 64
Then nobody will be in a group with anybody else more than once.
Edwin