# A2 math

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#1
Could someone please explain part a and b I don’t understand why they count over the squares when they are counting them therefore I can’t understand why the answers are the ones given . Also part 2 shows the addition of the squares I can’t see how this worked I can see how they’ve used the previous answers
Last edited by Danyal124; 3 months ago
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3 months ago
#2
One 8*8 square
Four 7*7 squares
Nine 6*6 squares
....

The 8*8 one is obvious.
Consider placing a 7*7 square. On each axis 1..8 it must cover 7 intervals, so there are two possibilities 1..7 and 2..8. So two possible placements in each of the two axes, so four placements in the 2D grid in total.
Similar for the rest. So for a 6*6 square, on each axis it will fill one of three possibilities 1..6, 2..7 or 3..8. So nine possible placements on the 2D grid.

Get in the habit of drawing out smaller (simpler) grids 2*2, 3*3, 4*4 and verify that it's right, if you don't understand the more complex case.

Part b) the wording is a bit loose,but they want to find the total number of different squares that can be placed on a grid. Different refers to size and position, so sum up all the (squares) values in part a) as these consider all possible squares.
Last edited by mqb2766; 3 months ago
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#3
(Original post by mqb2766)
One 8*8 square
Four 7*7 squares
Nine 6*6 squares
....

The 8*8 one is obvious.
Consider placing a 7*7 square. On each axis 1..8 it must cover 7 intervals, so there are two possibilities 1..7 and 2..8. So two possible placements in each of the two axes, so four placements in the 2D grid in total.
Similar for the rest. So for a 6*6 square, on each axis it will fill one of three possibilities 1..6, 2..7 or 3..8. So nine possible placements on the 2D grid.

Get in the habit of drawing out smaller (simpler) grids 2*2, 3*3, 4*4 and verify that it's right, if you don't understand the more complex case.

Part b) the wording is a bit loose,but they want to find the total number of different squares that can be placed on a grid. Different refers to size and position, so sum up all the (squares) values in part a) as these consider all possible squares.
im finding it diffucult to understand what youre explaing ive read over it and still i can see the 8 by 8 and understand the 7 by 7 but for the 6 by 6 theres 3 placements on one axes and 3 on the other isnt that 6 altogheter
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3 months ago
#4
(Original post by Danyal124)
im finding it diffucult to understand what youre explaing ive read over it and still i can see the 8 by 8 and understand the 7 by 7 but for the 6 by 6 theres 3 placements on one axes and 3 on the other isnt that 6 altogheter
No. 3*3 placements for the six by six tiles gives 9, not 6.
If you do the simpler/smaller cases as suggested, it should be clear why this is the case.
Last edited by mqb2766; 3 months ago
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