Welcome to Ian’s Friday Puzzle! Dust off those Friday cobwebs with a little manipulation of the old grey matter. Perplexing puzzles, logical, illogical, and sometimes just plain stupid. Be prepared to be bewildered, befuddled and bedazzled!
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A large square is split into four congruent squares, two are shaded yellow.
The other two squares have smaller yellow squares in them, whose vertices are the midpoints of the sides of the unshaded squares.
What fraction of the large square is shaded?
The diagram shows six identical squares, each with side length 10 cm, arranged symmetrically.
What area of the diagram is shaded?
Hence what fraction of the diagram is shaded?
Using only the digits 1 to 9, place them in the baubles around the Christmas tree.
The sum on the outside of the tree must be DOUBLE that of the inside triangle.
A circle is divided into five equal sectors as shown.
What is the ratio of the length of the perimeter of one of these sectors to the length of the circumference of the circle?
A circle has three equal smaller circles whose centres
are placed on its diameter as shown.
Which area is bigger, the three shaded circles or
one of the two equal unshaded areas?
Colin and his daughters Abigail and Brenda have the same birthday.
Today, Colin is 28, Abigail is 6 and Zoey is 2.
How old will Colin be when his age is the sum of the ages of Abigail and Brenda?
The diagram shows an equilateral triangle inside a regular hexagon.
The hexagon has sides of length 10 cm.
The vertices of the triangle are midpoints of sides of the hexagon.
What is the length of the perimeter of the triangle?
Two circles of radius 2 cm fit exactly between two parallel lines, as shown in the diagram.
The centres of the circles are 6 cm apart.
What is the area that is shaded yellow?
A positive integer has exactly eight factors.
Two of these factors are 14 and 22.
What is the sum of all eight factors of the positive integer?
The England T20 Cricket team are messing about.
Jason thinks of a positive integer, which Jos then doubles.
Dawid then trebles Jos’ number.
Finally Jonny multiplies Dawid’s number by six.
Eoin notices that the sum of the four numbers is a perfect square!
What is the smallest number that Jason could have thought of?