Puzzle 1
How many squares, of any size, can you find on this chessboard that do not contain a rook?
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
Share link – www.brainbashers.com/puzzle/zukb
Hint
The largest square is 4x4 small squares.
Answer
There are 110 squares without a rook.
Reasoning
There are 60 squares of size 1x1.
There are 35 squares of size 2x2.
There are 12 squares of size 3x3.
There are 3 squares of size 4x4.
A total of 60 + 35 + 12 + 3 = 110.
Puzzle 2
How many squares, of any size, can you find on this chessboard that do not contain a rook?
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
Share link – www.brainbashers.com/puzzle/zylq
Hint
How many 1 x 1 squares are there?
Answer
There are 116 squares without a rook.
1 x 1: 61 squares.
2 x 2: 37 squares.
3 x 3: 15 squares.
4 x 4: 3 squares.
Puzzle 3
How many squares, of any size, can you find on this chessboard that do not contain a rook?
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
Share link – www.brainbashers.com/puzzle/zdpx
Hint
There are no squares of size 5x5.
Answer
125.
Reasoning
There are 61 squares of size 1x1.
There are 39 squares of size 2x2.
There are 20 squares of size 3x3.
There are 5 squares of size 4x4.
A total of 61 + 39 + 20 + 5 = 125.
Puzzle 4
How many squares, of any size, can you find on this chessboard that do not contain a rook?
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
Share link – www.brainbashers.com/puzzle/zrzl
Hint
How many 2 x 2 squares are there?
Answer
128.
Reasoning
There are 62 squares of size 1 x 1.
There are 41 squares of size 2 x 2.
There are 18 squares of size 3 x 3.
There are 6 squares of size 4 x 4.
There is 1 square of size 5 x 5.
A total of 62 + 41 + 18 + 6 + 1 = 128.
Puzzle 5
How many squares, of any size, can be found on a standard chessboard?
How many rectangles, of any size, can be found on a standard chessboard?
Remember when counting the rectangles, that squares are also rectangles.
workings
hint
answer
print
Share link – www.brainbashers.com/puzzle/zlyw
Hint
How many 8x8 squares are there, what about 7x7.
Answer
1,296 rectangles and 204 squares.
Puzzle 6
What is the minimum number of queens required on a chessboard such that all squares are attacked?
workings
hint
answer
print
Share link – www.brainbashers.com/puzzle/zucz
Hint
Try this with a real board.
Answer
5.
Puzzle 7
How many squares, of any size, can you find on this chessboard which do not contain a rook?
Puzzle Copyright © Kevin Stone
workings
hint
answer
print
Share link – www.brainbashers.com/puzzle/zxqo
Hint
How many 2x2 squares are there?
Answer
93.
There are 60 squares of size 1x1.
There are 33 squares of size 2x2.
A total of 60 + 33 = 93.
Note: BrainBashers has a Dark Mode option – I recommend not using your browser's dark mode or extensions for BrainBashers
