puzzle from 1980 book :
1 :
write code that calculates the number of squares in any rectangle
the recangle is filled totaly
no squares overlap
input is width and height of the rectangle
2 :
find the smalest rectangle whit that
square chalence
Re: square chalence
I don't know if I understand the question.
Surely if w is a rational multiple of h we can cover the rectangle with many different square tesselations. And if not, no covering is possible without leaving gaps.
Suppose mw = nh where m and n are both positive integers. Then we can cover the rectangle with squares of side length s = w/n = h/m.
But we can also do it with squares of side length s/2, s/3, s/4 and so on.
The second part of your question is incomprehensible.
Surely if w is a rational multiple of h we can cover the rectangle with many different square tesselations. And if not, no covering is possible without leaving gaps.
Suppose mw = nh where m and n are both positive integers. Then we can cover the rectangle with squares of side length s = w/n = h/m.
But we can also do it with squares of side length s/2, s/3, s/4 and so on.
The second part of your question is incomprehensible.
Re: square chalence
sizes are integers
find the smalles retangle that fits the puzle
find the smalles retangle that fits the puzle
Re: square chalence
1. Smallest number of squares that will completely and nonoverlappingly cover a rectangle of given integer width and height
edit: smallest number of squares of equal size
2. w=h=1 is the smallest rectangle with integer side lengths that can be totally covered by some number of squares. Again, I don't think this question makes sense.
Code: Select all
function gcd( w as uinteger, h as uinteger ) as uinteger
if h = 0 then
return w
else
return gcd(h, w mod h)
end if
end function
dim as uinteger w, h, g
input w, h
g = gcd(w, h)
print w*h/(g*g)
2. w=h=1 is the smallest rectangle with integer side lengths that can be totally covered by some number of squares. Again, I don't think this question makes sense.
Last edited by thebigh on Apr 02, 2020 16:13, edited 1 time in total.
Re: square chalence
more that 1 square is good