I travelled from London to Glasgow last week at 60 miles per hour, I had filled my petrol tank just before I left, and it was full to the brim (25 gallons).
Unfortunately, my petrol tank sprang a leak immediately, and I only managed to drive 300 miles before I ran out of petrol.
My car does 30 miles per gallon, how fast was I losing petrol through the hole?
Triangle: 47. Doughnut
The area of a circle is π x Radius2.
The larger circle has diameter = 40, therefore, the radius is 20, and the area is π x 202 = 400π.
The smaller circle has diameter = 20, therefore, the radius is 10, and the area is π x 102 = 100π.
Therefore, the shaded area is 400π − 100π = 300π ≈ 942. Circle
The area of a circle is π x Radius2.
The circle with diameter 31 has a radius of 15.5 and an area of π x 15.52 ≈ 755.
The circle with diameter 35 has a radius of 17.5 and an area of π x 17.52 ≈ 962 (closest match).
The circle with diameter 39 has a radius of 19.5 and an area of π x 19.52 ≈ 1195. Square
The area of a square is Side x Side.
The square with side 31 has an area of 31 x 31 = 961 (closest match).
The square with side 35 has an area of 35 x 35 = 1225.
The square with side 39 has an area of 39 x 39 = 1521. Triangle
The area of a triangle is 1/2 x Base x Height. Using Pythagoras' theorem, it can be shown that the area of an equilateral triangle is √3 x Base2 ÷ 4.
The triangle with side 39 has an area of √3 x 39 x 39 ÷ 4 ≈ 659.
The triangle with side 43 has an area of √3 x 43 x 43 ÷ 4 ≈ 801.
The triangle with side 47 has an area of √3 x 47 x 47 ÷ 4 ≈ 957 (closest match).
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Puzzle 15
Customer services at BrainBashers headquarters received the following letter recently.
Luckily our top puzzle solvers were able to determine the meaning and help Mrs Middins.
Answer
The letter was written on a typewriter which has a problem with the middle row of letters, which print spaces instead. The letter should have read:
Dear Sir,
I recently visited one of your outlets to buy one of your typewriters. However, as you can see I am having a small problem.
The middle row of the keyboard appears to be faulty.
I would be very grateful if you could despatch a replacement by return post. Failing this, could you please send an engineer to resolve this problem as a matter of urgency.
Yours faithfully,
Mrs Middins.
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Puzzle 16
What is the minimum number of queens required on a chessboard such that all squares are attacked?
