This investigation is about the number of coloured squares on a chequered flag.A chequered flag has two or more colours making a pattern of squares.There is always a black square in the top left corner.The size of a flag is m by n, where m is the number of rows and n is the number of columns.1 (a) The flag above is a 4 by 5, black and white chequered flag.Write down the number of black squares and the number of white squares.Black .....................................................White .....................................................(b) (i) Complete both tables.Size of flag2 by 1 2 by 2 2 by 3 2 by 4 2 by 5 2 by nBlack 1 2White 1 2Size of flag4 by 1 4 by 2 4 by 3 4 by 4 4 by 5 4 by nBlack 2White 2
Question
This investigation is about the number of coloured squares on a chequered flag.A chequered flag has two or more colours making a pattern of squares.There is always a black square in the top left corner.The size of a flag is m by n, where m is the number of rows and n is the number of columns.1 (a) The flag above is a 4 by 5, black and white chequered flag.Write down the number of black squares and the number of white squares.Black .....................................................White .....................................................(b) (i) Complete both tables.Size of flag2 by 1 2 by 2 2 by 3 2 by 4 2 by 5 2 by nBlack 1 2White 1 2Size of flag4 by 1 4 by 2 4 by 3 4 by 4 4 by 5 4 by nBlack 2White 2
Solution
(a) For a 4 by 5 chequered flag, there are 10 black squares and 10 white squares.
(b) (i) The completed tables are:
Size of flag: 2 by 1, 2 by 2, 2 by 3, 2 by 4, 2 by 5, 2 by n Black: 1, 2, 2, 3, 3, n/2 (rounded up to the nearest whole number) White: 1, 2, 2, 3, 3, n/2 (rounded down to the nearest whole number)
Size of flag: 4 by 1, 4 by 2, 4 by 3, 4 by 4, 4 by 5, 4 by n Black: 2, 4, 6, 8, 10, 2n White: 2, 4, 6, 8, 10, 2n
Please note that for the 2 by n flag, the number of black and white squares depends on whether n is even or odd. If n is even, there will be an equal number of black and white squares. If n is odd, there will be one more black square than white squares.
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