Puzzle 29
Which four vegetables have been merged together?
cab swe rpr eed oaa etn
Puzzle Copyright © Kevin Stone
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Hint
The first letters of the words are: C, S, P, B. One of the vegetables is another word for rutabaga.
Answer
Carrot, swede, pea, bean.
Swede is another word for rutabaga.
Puzzle 30
My local library decided to hand out some of its old books to the 1,400 people who lived in the town.
To each library member, they offered 6 books, and to each non-member, they offered 4 books.
If only half of the members, and three-quarters of the non-members, accepted the books, how many books were given away?
Puzzle Copyright © Kevin Stone
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Hint
As we don't know how of the people were library members, you can try a random number and see what happens.
Answer
4,200 books.
Reasoning
It doesn't matter how many library members there were, as 1/2 of them accepted the books, and each accepted 6 books, which is 3 books per member on average.
Similarly, it doesn't matter how many non-members there were as 3/4 of them accepted the books, and each accepted 4 books, which is again 3 books per non-member on average.
Double-Checking
Both the members and non-members accepted, on average, 3 books each.
And 1400 x 3 = 4200.
Puzzle 31
What number comes next in this sequence:
914275 94275 9475 975 {?}
Puzzle Copyright © Kevin Stone
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Hint
Take a close look at the digits.
Answer
97.
Reasoning
The lowest digit is removed each time.
Puzzle 32
Which circle, square, and triangle, have the closest area to the blue doughnut shape?
The drawings are to scale, so you might be able to judge by eye, or you can work out the actual areas.
Puzzle Copyright © Kevin Stone
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Hint
The area of a circle is π x Radius2.
Answers
Circle: 35.
Square: 31.
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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