Puzzle 37
If
7/28 of 64 is 16 and
9/12 of 100 is 75 and
3/9 of 33 is 11
what is 5/15 of 45?
Puzzle Copyright © Kevin Stone
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Hint
This is easier than it might first appear.
Answer
15.
Using normal mathematics!
Puzzle 38
After a day picking strawberries I had a basket full.
I ate 5 and gave Alex half of the remaining.
I then ate another 3 and gave Billie one third of the remaining.
I ate another 6 and then gave Charlie two thirds of the remaining.
I now had 34 strawberries left. How many did I start with?
Puzzle Copyright © Kevin Stone
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Hint
What fraction of them did I eat?
Answer
335 strawberries.
Working backwards...
I ended up with 34 strawberries, so I had 102 before giving Charlie two thirds.
I ate 6 myself, so I had 108 before I ate those.
I had 108 strawberries, so I had 162 before giving Billie one third.
I ate 3 myself, so I had 165 before I ate those.
I had 165 strawberries, so I had 330 before giving Alex one half.
Ate 5 myself, so I had 335 before I ate those.
Therefore I started with 335 strawberries.
Puzzle 39
You have a very large number of generic plastic building blocks, each in the shape of a cube.
Think about how many cubes you would need in order to construct a giant cube with 16 small cubes along each edge.
If you were to then remove the outside layer, how many small cubes would you have removed?
Puzzle Copyright © Kevin Stone
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Hint
Think about one face at a time.
Answer
1,352 small cubes.
Reasoning
The original large cube with 16 small cubes along each edge would require 16 x 16 x 16 = 4,096 small cubes.
Removing the outside layer would leave a large cube now with 14 small cubes along each edge (which requires 14 x 14 x 14 = 2,744 small cubes).
It isn't 15 small cubes because you're removing both ends of an edge.
Therefore, you have removed 4,096 - 2,744 = 1,352 small cubes.
Puzzle 40
Which square, which circle, and which triangle has the closest area to the doughnut shape on the left?
The drawings are to scale, so you might be able to judge it, as well as working the actual areas out.
Puzzle Copyright © Kevin Stone
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Hint
The area of a circle is π x Radius2.
Answer
Circle: 3.5.
Square: 3.1.
Triangle: 4.7.
Doughnut
The area of a circle is π x Radius2.
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).
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