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 111
Below are seven clues to seven words.
When arranged in the correct order, each word is an anagram of the previous word with a letter removed.
capital of Francesnakelong root vegetablesingle articletwisted anklecoarse fileequally
Hint
The answer to 'long root vegetable' is the longest word.
Answers
parsnip = long root vegetable
sprain = twisted ankle
Paris = capital of France
rasp = coarse file
asp = snake
as = equally
a = single article
???
Puzzle 112
During the recent BrainBashers cipher convention, a binary code contest took place.
The contest consisted of a binary code transmission where the spaces between the letters were missing and there was no punctuation.
Each letter of the alphabet was translated into its binary equivalent based on its position in the alphabet. The resulting code was then blocked in groups of five digits.
a=1, b=10, c=11, d=100, e=101, f=110, g=111, h=1000, i=1001, j=1010, k=1011, l=1100, m=1101, n=1110, o=1111, p=10000, q=10001, r=10010, s=10011, t=10100, u=10101, v=10110, w=10111, x=11000, y=11001, z=11010
