How many ways can 25 pieces of varying shapes fit in a square space?

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To determine how many combinations of 25 pieces of varying shapes can fit into a square space, the specific quantities of each shape must be considered. The pieces include 7 medium squares, 3 large squares, 5 small squares, 2 long narrow rectangles, 4 medium rectangles, and 4 short narrow rectangles. The arrangement possibilities depend on the spatial constraints and the ability to place the shapes anywhere within the square. Calculating the combinations requires a clear understanding of the shapes' dimensions and how they interact within the given area. Ultimately, the solution hinges on the distribution and arrangement of these shapes within the defined space.
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I have a total of 25 pieces in 6 different shapes to fit in a given space. How many combinations can the pieces be put together to fit in the same given space?
 
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Homework Statement

I have 25 items total in 6 different shapes that all fit into a a given space. How many combinations can the 25 items fit into the same size space?

Homework Equations



Not sure

The Attempt at a Solution



Not sure
 
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You'd need to know how many of each of the 6 possible shapes there are, and if any of the shapes can go anywhere.
 
'Not sure' is right. I'm not even sure that's grammatical. Can you state that more clearly?
 
Yes, they can be placed anywhere within the space. (square shaped space) There are 7 medium sized squares, 3 large squares, 5 small squares, 2 long narrow rectangles, 4 medium rectangles and 4 short narrow rectangles.
 

Thread 'Find the polar form of a complex number'

The working out suggests first equating ## \sqrt{i} = x + iy ## and suggests that squaring and equating real and imaginary parts of both sides results in ## \sqrt{i} = \pm (1+i)/ \sqrt{2} ## Squaring both sides results in: $$ i = (x + iy)^2 $$ $$ i = x^2 + 2ixy -y^2 $$ equating real parts gives $$ x^2 - y^2 = 0 $$ $$ (x+y)(x-y) = 0 $$ $$ x = \pm y $$ equating imaginary parts gives: $$ i = 2ixy $$ $$ 2xy = 1 $$ I'm not really sure how to proceed from here.
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