square chalence

[bluatigro]

puzzle :
write a program that finds the smalest square
filled whit all different squares

[bluatigro]

pardon me

the puzzle is realy
find for every near square the least number of differen sised
what wil fit in it [ retangle must be totaly coverred ]
no two squares wil overlap

input of code is width and height of retangle

i got this from a book [ 1980 ]

[B+]

Here is my solution:


'Min Squares That Fit Inside a Rectangle.txt for JB v2.0 b+ 2020-04-01
global INDEX
do
   print "We are going to list all the squares that fill in a rectangle."
   Input "0 quits, Enter width of the rectangle with integer sides: ";w
   Input "0 quits, Enter height of the rectangle with integer sides: ";h
   print
   dim amts(100), sides(100), areas(100)
   INDEX = 0 : totalArea = 0 : totalAmts = 0
   if w > 0 and h > 0 then
       Print "The squares that fit in a ";w;"X";h;" rectangle are:"
       call reduceRectangleByLargestSquare w, h
       for i = 1 to INDEX
           print amts(i);" Square(s) of size ";sides(i);"X";sides(i);" has area of ";areas(i)
           totalAmts = totalAmts + amts(i) : totalArea = totalArea + areas(i)
       next
       print "========================================================================"
       print "Total squares is ";totalAmts;", total of square areas is ";totalArea;"."
       print "Area of rectangle ";w;"X";h;" is ";w * h;"."
       print
   else
       print "That's not a rectangle."
       print
   end if
   print
loop until w = 0 or h= 0
print "Bye!"
end

sub reduceRectangleByLargestSquare w, h  ' <<<< recursive sub
   if w <> 0 and h <> 0 then
       if w < h then
           INDEX = INDEX + 1
           amts(INDEX) = int(h/w) : sides(INDEX) = w : areas(INDEX) = w * w * int(h/w)
           'print int(h/w);" Square(s) of size ";w;"X";w
           nH = h - int(h/w) * w
           nW = w
           if nH = 0 then
              exit sub
           else
              call reduceRectangleByLargestSquare nH, nW
           end if
       else
           INDEX = INDEX + 1
           amts(INDEX) = int(w/h) : sides(INDEX) = h : areas(INDEX) = h * h * int(w/h)
           'print int(w/h);" Square(s) of size ";h;"X";h
           nW = w - int(w/h) * h
           nH = h
          if nW = 0 then
               exit sub
           else
              call reduceRectangleByLargestSquare nH, nW
           end if
    end if
   end if
end sub


Sample Output:

We are going to list all the squares that fill in a rectangle.
0 quits, Enter width of the rectangle with integer sides: 100
0 quits, Enter height of the rectangle with integer sides: 57

The squares that fit in a 100X57 rectangle are:
1 Square(s) of size 57X57 has area of 3249
1 Square(s) of size 43X43 has area of 1849
3 Square(s) of size 14X14 has area of 588
14 Square(s) of size 1X1 has area of 14
========================================================================
Total squares is 19, total of square areas is 5700.
Area of rectangle 100X57 is 5700.

[B+]

OK now I get it. Pick two sequential Fibonacci Numbers and you have a bunch of unique squares filling out the rectangle:

0 quits, Enter width of the rectangle with integer sides: 4181
0 quits, Enter height of the rectangle with integer sides: 2584

The squares that fit in a 4181X2584 rectangle are:
1 Square(s) of size 2584X2584 has area of 6677056
1 Square(s) of size 1597X1597 has area of 2550409
1 Square(s) of size 987X987 has area of 974169
1 Square(s) of size 610X610 has area of 372100
1 Square(s) of size 377X377 has area of 142129
1 Square(s) of size 233X233 has area of 54289
1 Square(s) of size 144X144 has area of 20736
1 Square(s) of size 89X89 has area of 7921
1 Square(s) of size 55X55 has area of 3025
1 Square(s) of size 34X34 has area of 1156
1 Square(s) of size 21X21 has area of 441
1 Square(s) of size 13X13 has area of 169
1 Square(s) of size 8X8 has area of 64
1 Square(s) of size 5X5 has area of 25
1 Square(s) of size 3X3 has area of 9
1 Square(s) of size 2X2 has area of 4
2 Square(s) of size 1X1 has area of 2
========================================================================
Total squares is 18, total of square areas is 10803704.
Area of rectangle 4181X2584 is 10803704.


Not only that but they are all Fibonacci Numbers!

[bluatigro]

only 1 square of eatch size !!