This problem solving activity has a logic and reasoning focus.
Miriama is building a large square window made up of 16 red and white panes.
What is the smallest number of red panes she can put into the window so that no three of them are in any row or column and so that she cannot put in another red pane without three being in the same row or column?
This problem requires students to use a systematic approach in order to be able to justify that all possibilities have been considered.
The problem also challenges students to recognise the symmetry in a figure, and to see that by rotating a figure through a quarter turn either clockwise or anticlockwise, two 'answers' are essentially the same. Symmetry through a line in the plane of the square is therefore important.
See also these Logic and Reasoning problems: Strawberry Milk, Level 1; Strawberry and Chocolate Milk, Level 1; Three-In-A-Line, Level 2; No Three-In-A-Line, Level 3; No-Three-In-A-Line Again, Level 5; and No-Three-In-A-Line Game, Level 6.
Miriama is building a large square window made up of 16 red and white panes.
What is the smallest number of red panes she can put into the window so that no three of them are in any row or column and so that she cannot put in another red pane without three being in the same row or column?
(a) Miriama now wants to put 25 panes in her red and white window.
What is the smallest number of red panes she can put into the window so that no three of them are in any row or column and so that she cannot put in any more red panes without three being in the same row or column?
(b) Miriama wants to make a square window made up of 16 red and white panes. What numbers of red panes can she put into the window so that no three of them are in any row or column and so that she cannot put in another red pane without three being in the same row or column?
In the same way as No-Three-In-A-Line Again, Level 5, we can show that three won’t work. However, 4 will and in two ways. This can be justified by working systematically. The two possible answers are shown below.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/no-more-line at 9:00pm on the 26th February 2024