Cover a square with rectangles P69283
Suppose that you have an infinite suply of m × 2m rectangles for every natural m ≥ 1. You have to exactly cover an ℓ × ℓ square (you can choose ℓ ) by placing n of those rectangles horizontally or vertically. For instance, these are some ways for n = 2, n = 5 and n = 6:
linecolor=black
[fillcolor=blue,fillstyle=solid](0,0)(0,1)(2,1)(2,0) [fillcolor=red,fillstyle=solid](0,1)(0,2)(2,2)(2,1)
[fillcolor=blue,fillstyle=solid](4,0)(4,4)(6,4)(6,0) [fillcolor=yellow,fillstyle=solid](6,0)(6,2)(7,2)(7,0) [fillcolor=red,fillstyle=solid](7,0)(7,2)(8,2)(8,0) [fillcolor=green,fillstyle=solid](6,3)(6,4)(8,4)(8,3) [fillcolor=orange,fillstyle=solid](6,2)(6,3)(8,3)(8,2)
[fillcolor=cyan,fillstyle=solid](10,0)(10,4)(12,4)(12,0) [fillcolor=orange,fillstyle=solid](10,4)(10,6)(14,6)(14,4) [fillcolor=green,fillstyle=solid](14,2)(14,6)(16,6)(16,2) [fillcolor=red,fillstyle=solid](12,0)(12,2)(16,2)(16,0) [fillcolor=yellow,fillstyle=solid](12,2)(12,3)(14,3)(14,2) [fillcolor=blue,fillstyle=solid](12,3)(12,4)(14,4)(14,3)
There are only a few n for which it is impossible to cover a square with n such rectangles. In particular, it is always possible when n % 3 = 2. Can you prove it?
Input
Input consists of several n such that n ≡ 2 (mod 3 ). Assume 2 ≤ n ≤ 62.
Output
For every n, first print a line with an ℓ between 2 and 30. Afterwards, print ℓ lines with ℓ characters each. Use different digits, lowercase letters and uppercase letters to indicate each rentangle. Since there are multiple possible solutions, print any one.
Input
2 2 14
Output
2 00 11 6 ZZZaaa ZZZaaa ZZZaaa ZZZaaa ZZZaaa ZZZaaa 8 C3POjj42 C3POdd42 BBBBBBBB BBBBBBBB BBBBBBBB BBBBBBBB T1111XX5 T1111YY5
- Author
- Salvador Roura
- Language
- English
- Official solutions
- C++
- User solutions
- C++