How many different digits are needed to fill an NxN grid, such
that every pair of adjacent digits (horizontally and vertically)
is a unique pair? Solve for N=2,3,4,5,6. Give examples.
For example, for N=2, three digits are needed:
00
12
This 2x2 grid has the four unique pairs 00, 01, 02, and 12.
How many different digits are needed to fill an NxN grid,
such that no pair of digits can be found adjacent in the grid more
than twice? Solve for N=2,3,4,5,6.
How many different digits are needed to fill an NxN grid,
such that no pair of digits can be found adjacent in the grid more
than three times? Solve for N=2,3,4,5,6.
My extended question for this is,
Can a set of double-5 dominoes (minus 3 dominoes) fill a 6x6 grid
such that no pair of digits can be found adjacent more than three times?