Puzzle 17
How many squares of any size on this chessboard do not contain a rook?
Puzzle Copyright © Kevin Stone
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Hint
There are no squares of size 5 x 5.
Answer
There are 125 squares without a rook.
Reasoning
61 squares of size 1 x 1
39 squares of size 2 x 2
20 squares of size 3 x 3
5 squares of size 4 x 4
Giving a total of 61 + 39 + 20 + 5 = 125 squares.
Puzzle 18
During a recent BrainBashers race meeting, the fastest driver managed to complete a lap with an average speed of 150 mph.
They managed to complete the first two fifths of the lap at a speed of 123 mph and the second two fifths of the lap at a speed of 164 mph.
At what speed was the final one fifth of the lap length covered?
The answer is not 176 mph.
Puzzle Copyright © Kevin Stone
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Hint
Adding the speeds won't work.
Answer
205 mph.
Reasoning
If we take the number of miles in a lap to be L miles and use Time = Distance ÷ Speed.
The first 2/5 are covered at 123 mph. Therefore, the time taken was [(2/5) x L] ÷ 123 hours.
The next 2/5 are covered at 164 mph. Therefore, the time taken was [(2/5) x L] ÷ 164 hours.
The last 1/5 is covered at y mph. Therefore, the time taken was [(1/5) x L] ÷ y hours.
The entire trip is covered at an average of 150 mph, and we can conclude that:
2L 2L L L
————— + ————— + ——— = ———
5x123 5x164 5y 150
Rearranging and simplifying gives:
1 1 2 2
——— = —— - ——— - ———
y 30 123 164
That means that y = 1 ÷ (1/30 − 2/123 − 2/164)
Using a calculator gives y = 205.
Puzzle 19
Which of the shapes is identical to the first one?
There might be more than one.
Puzzle Copyright © Robert A. Hartmann
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Hint
Try to rotate them around in your head, but watch out for mirror images.
Puzzle 20
What letter comes next in this sequence:
E · O · E · R · E · ?
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Hint
This is a very common sequence.
Answer
X.
The last letters of the words one, two, three, four, five, six.