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How can I find the number of the smallest possible square that can fit in a given square

suppose that I have a square of 7x7.i can fill the square with other squares (i.e., squares of dimension 1x1,2x2 ..... 6x6). How can I fill a square with the least possible smaller squares. please help me.

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Consider a square with dimensions s x s. Cutting a smaller square of sizes m x mout will result in a square m x m, a square, n x nand two size rectangles m x n, where m + n = s.

When seven, the square can be divided so that m = n, in this case, the rectangles will also be squares, which will give an answer of 4.

, s , m n , . , , , m x n ( , , ). 2 x ([number of squares in m x n rectangle] + 1). m 1 s/2.

, .

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s x s. s . sp. sp x sp, s x s. , . , 17 x 17. s, 4.

:

n = (s + 1)/2, , n = s-1.

n x n .

m = s - n. m x m , () n x n.

m x m ( ) 2m-1 x 2m-1 .

. n2 x n2 , .

, :

s  minimum number of squares:
2   4
3   6
5   8
7   9
11  10
13  11
17  12
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, n. n , , 3 2 , ,

, : ,

" " , , , , . , . , , , .

, (n1,n2,n3), n1 + n2 + n3 = n n1, n2, n3 (> = 2) n >= 7 n1 <= n2 <= n3

:

My algorithm

- (n1,n2,n3), , . n_s = n1 + n2. n_s > n3 , n_s n3

, angular ( ).

n4 x n3 angular, :

n4 = n - 2 * n3 \\if following the depicted example

(n41, n42, n43) ( n n = n4, n3> = 7) (n31, n32, n33) ( n n = n3, n3> = 7). , n_s3 == n_s4 , .
:

, x3 = 17 x4 = 13

  Enumeration of x3 = 17:
  2 + 2 + 13
  3 + 3 + 11
  5 + 5 + 7

  Enumeration of x_s3:
  4 = 2 + 2
  6 = 3 + 3
  10 = 5 + 5
  12 = 5 + 7
  14 = 3 + 11
  15 = 2 + 13

  Enumeration of x4 = 13:
  2 + 2 + 7
  3 + 5 + 5

  Enumeration of x_s4:
  4 = 2 + 2
  8 = 3 + 5
  9 = 2 + 7
  10 = 5 + 5

10 , 13 17, 10 10 ( angular), , , ( ) .

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