Originally posted by bellyflop
a)Indiana has a rectangular board 14cm x 15cm and a large supply of rectangular stamps in two sizes, 4cm x 3cm and 5cm x 2cm. She dicises to cover the board exactly with some of the stamps in any orientation, but with no gaps,cute or overlaps.She may use either kind or mixture of both.
Find all the differesnt selections of stamps Indiana can use and illus ...[text shortened]... nnot cover the board exactly with these stamps in any orientation, with no gaps,cute or overlaps
Consider the length 6 sides of the 11*6 cm board. The combinations of card edges that can span this are (i) 3 2cm edges, ii) 2 3cm edges or iii) a 2cm edge plus a 4cm edge. We need 2 of these combinations to cover both 6 length sides.
if we try combinations i) and ii) we are left with a 6*2 cm piece of board, to cover with a 4*3 card, which doesn't work.
We can't use both combinations i) and iii) because we would need one more 2*cm stamp than we have, equally we can't use 1) twice or ii) twice because we haven't got enough stamps.
If we try ii) and iii) we find we have a 2cm wide chunk that is only 4 cm heigh: too small for any stamp.
and if we try iii) twice we can't put the two 5*2cm stamps opposite each other because an uncoverable 1cm wide piece of board is left. If altrenatively we offset the two 5*2cm stamps we are left with a zig-zag shaped bit of board which can't be covered with the remaining two stamps.
So there is no way to cover the board.