Puzzle 29
What number comes next in this sequence:
3 3 5 4 4 3 5 {?}
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Hint
This is a very common sequence.
Answer
5.
The numbers represent the number of letters of the words ONE, TWO, THREE, etc. Therefore the answer is the number of letters in the word EIGHT.
Puzzle 30
What value of X makes the following correct:
Puzzle Copyright © Kevin Stone
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Hint
The answer is a whole number less than 10.
Answer
3.
Reasoning
We can multiply throughout by 12,
X X X X
- - - + - = -
X 2 4 12
to give:
12 - 6X + 3X = X
12 - 3X = X
12 = 4X
3 = X
As required.
Double-Checking
3 3 3 3
- - - + - = -
3 2 4 12
1 - 1.5 + 0.75 = 0.25
0.25 = 0.25, which confirms that 3 is correct.
Puzzle 31
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).
Puzzle 32
From 6523 grows a plant.
I 689, I 689, I 689, it's no joke.
751 rhymes with you.
421 rhymes too!
What am I?
Puzzle Copyright © Kevin Stone
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Hint
What 4-letter word does a plant grow from?
Answer
Wednesday.
Reasoning
Each number in the poem indicates which letter of the answer is being used.
6523 = seed
689 = say
751 = dew
421 = new
Therefore, '751 rhymes with you' is read as 'dew rhymes with you'.
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