04 Mar 09
Originally posted by PalynkaI worked out that it is 1092.
What about the number of rectangles?
If you think of a rectangle of 1 square by 2 (1x2). That can go 7 across and 8 down (or vice versa) so that is 8*7 times it fits in the 64 squares.
For the others:
1x3=6*8
1x4=5*8
1x5=4*8
1x6=3*8
1x7=2*8
1x8=1*8
2x3=6*7
2x4=5*7
2x5=4*7
2x6=3*7
2x7=2*7
2x8=1*7
3x4=5*6
3x5=4*6
3x6=3*6
3x7=2*6
3x8=1*6
4x5=4*5
4x6=3*5
4x7=2*5
4x8=1*5
5x6=3*4
5x7=2*4
5x8=1*4
6x7=2*3
6x8=1*3
7x8=1*2
Simplified:
8(7+6+5+4+3+2+1) + 7(6+5+4+3+2+1) + 6(5+4+3+2+1) + 5(4+3+2+1) + 4(3+2+1) + 3(2+1) + 2
8*28 + 7*21 + 6*15 + 5*10 + 4*6 + 3*3 + 2 = 224 + 147 + 90 + 50 + 24 + 9 + 2 = 546
This is for the rectangles going in one direction, for the other direction, multiply by 2 to get 1092.
04 Mar 09
Originally posted by lauseyAren't squares rectangles?
I worked out that it is 1092.
If you think of a rectangle of 1 square by 2 (1x2). That can go 7 across and 8 down (or vice versa) so that is 8*7 times it fits in the 64 squares.
For the others:
1x3=6*8
1x4=5*8
1x5=4*8
1x6=3*8
1x7=2*8
1x8=1*8
2x3=6*7
2x4=5*7
2x5=4*7
2x6=3*7
2x7=2*7
2x8=1*7
3x4=5*6
3x5=4*6
3x6=3*6
3x7=2*6
3x8=1*6 ...[text shortened]... s for the rectangles going in one direction, for the other direction, multiply by 2 to get 1092.