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'Table Patterns Go Wild!' printed from http://nrich.maths.org/
Nearly all of us have made table patterns on hundred squares, that
is $10$ by $10$ grids. Some tables made vertical lines, some made
diagonal lines and some patterns ranging across the whole space.
Hundred squares are $10$ by $10$ grids. In this problem we will
call these "$10$ grids".
What numbers made which sort of patterns and why?
This problem looks at the patterns on differently sized square
grids. These are from $4$ grids (that is a $4$ by $4$ grid) to $9$
These are patterns on a $7$, a $5$, an $8$ and on a $6$ grid:
What tables made these patterns? Can you think why they made them
Perhaps this is the time to experiment for yourself. You can use
grids drawn on squared paper or use this sheet
Can you discover what makes vertical and diagonal lines on the
different grids and what makes the various patterns. Can you make
the checked pattern? What table do you need to use on what kind of
Here are the top parts of some grids.
Can you identify what table on what grid have been used to make
Here are some parts of various grids. This time we have not shown
the edges of the grids. Can you identify what tables on what grids
could have been used to make these patterns?
There may be more than one answer.