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The larger circle has diameter = 4, therefore the radius is 2, and the area is π x 22 = 4π.
The smaller circle has diameter = 2, therefore the radius is 1, and the area is π x 12 = π.
Therefore the shaded area is 4π - π = 3π ≈ 9.42.
Circle
The area of a circle is π x Radius2.
The circle with diameter 3.1 has a radius of 1.55 and an area of π x 1.552 = 7.55.
The circle with diameter 3.5 has a radius of 1.75 and an area of π x 1.752 = 9.62 (** closest match).
The circle with diameter 3.9 has a radius of 1.95 and an area of π x 1.952 = 11.95.
Square
The area of a square is Side x Side.
The square with side 3.1 has an area of 3.1 x 3.1 = 9.61 (** closest match).
The square with side 3.5 has an area of 3.5 x 3.5 = 12.25.
The square with side 3.9 has an area of 3.9 x 3.9 = 15.21.
Triangle
The area of a triangle is ½ x Base x Height. Using Pythagoras' theorem it can be shown that the area of an equilateral triangle is Sqrt(3) x Base2 ÷ 4.
The triangle with side 3.9 has an area of Sqrt(3) x 3.9 x 3.9 ÷ 4 = 6.59.
The triangle with side 4.3 has an area of Sqrt(3) x 4.3 x 4.3 ÷ 4 = 8.01.
The triangle with side 4.7 has an area of Sqrt(3) x 4.7 x 4.7 ÷ 4 = 9.57 (** closest match).
Puzzle 6
Alex, Blake, Charlie and Drew are all trapped on an island in the middle of a crocodile infested lake.
Luckily they have one crocodile repelling stick that just about protects up to two swimmers.
To get to safety a maximum of two swimmers can be in the water at any one time and they have to be together to benefit from the stick, and must swim at the pace of the slower swimmer.
The shore is 50 metres away and they can not throw the stick back, someone has to swim back with the stick until all four are safely on the shore.
Alex can swim the distance in 3 minutes
Blake can swim the distance in 7 minutes
Charlie can swim the distance in 13 minutes
Drew can swim the distance in 17 minutes
How long does the overall rescue take - the answer is not 43 minutes!
[Ref: ZFKO]
Hint: Alex and Blake swim first.
Answer:
Alex and Blake swim to shore 7 minutes
Alex returns 3 minutes
Charlie and Drew swim to shore 17 minutes
Blake returns 7 minutes
Alex and Blake swim to shore 7 minutes
Total 41 minutes.
Puzzle 7
Can you create a sentence that contains the word 'and' five times in a row?
Note: with no other word between each 'and'.
[Ref: ZDBT]
Hint: Quite a tricky little puzzle!
Answer:
I commissioned an artist to paint a sign for BrainBashers that said "BrainBashers Puzzles And Illusions", however, they made a terrible mistake.
The gaps between 'Puzzles' and 'And', and 'And' and 'Illusions' weren't the same, so the sign seemed oddly out of balance.
Puzzle 8
Below are thirteen 5 lettered words, each of which has had two of its letters removed.
In total these 26 letters are A-Z. The remaining letters in each word are in the correct order.
There are no words which are spelled differently based upon location (favour/favor, etc).
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Alex, Blake, Charlie and Drew are all trapped on an island in the middle of a crocodile infested lake.
Can you create a sentence that contains the word 'and' five times in a row?
