How many lines are needed to make exactly N squares? Solve for 1<=N<=15.
For example, to make five squares, six lines are needed (draw a 2x2 grid, to give four 1x1 squares and one 2x2 square.) But to make exactly four squares, seven lines are needed.
Easier Extension: What is the largest number of squares which can be drawn with M lines?
Source: Original.
1---0
| |
0---0
lines 4 squares 1
1---1---0
| | |
0---0---0
lines 5 squares 2
1---1---1---0
| | | |
0---0---0---0
lines 6 squares 3
1---0
| |
1---1---1---0
| | | |
0---0---0---0
lines 7 squares 4
2---1---0
| | |
1---1---0
| | |
0---0---0
lines 6 squares 5
2---1---0
| | |
1---1---1---0
| | | |
0---0---0---0
lines 7 squares 6
1---0
| |
2---1---0
| | |
1---1---1---0
| | | |
0---0---0---0
lines 8 squares 7
2---2---1---o
| | | |
| | | |
1---1---1---o
| | | |
| | | |
o---o---o---o
lines 7 squares 8
1---0
| |
2---2---1---0
| | | |
1---1---1---0
| | | |
0---0---0---0
lines 8 squares 9
2---2---0---0---0
| | | |
| | | |
2---1---1---0---0
| | | |
| | | |
1---1---0 0 0
| | | |
| | | |
0---0---0---0---0
lines 8 squares 10
2---1---0
| | |
2---2---1---0
| | | |
1---1---1---0
| | | |
0---0---0---0
lines 8 squares 11
2---1---0
| | |
2---2---1---0
| | | |
1---1---1---1---0
| | | | |
0---0---0---0---0
lines 9 squares 12
2---1---1---0---0
| | | |
| | | |
2---2---1---1---0
| | | | |
| | | | |
1---1---1---0---0
| | | |
| | | |
0---0---0---0 0
lines 9 squares 13
3---2---1---0
| | | |
2---2---1---0
| | | |
1---1---1---0
| | | |
0---0---0---0
lines 8 squares 14
3---2---1---0
| | | |
2---2---1---0
| | | |
1---1---1---1---0
| | | | |
0---0---0---0---0
lines 9 squares 15