ONE-EIGHTH STAGE 2025
Prempeh College: 62 points
Suhum SHTS: 37 points
Benkum SHS: 13 points
Mfantsipim School: 53 points
Anglican SHS, Kumasi: 37 points
Sogakope SHS: 24 points
Adisadel College: 82 points
St. Hubert Seminary SHS: 24 points
Serwaa Nyarko Girls' SHS: 24 points
ROUND 5 - RIDDLE
RIDDLE
I am a type of polygon.
For any polygon, I fit my outline in the most ways possible.
For any polygon, I have the largest number of axes of symmetry.
ANSWER: Regular polygon
EXPLANATION:
A regular polygon with $n$ sides has $n$ axes of symmetry.
It fits its outline in $2n$ ways, which is the most for an $n$-sided polygon.
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PRACTICE QUESTIONS
1. RIDDLE:
I am a plane figure.
I am a polygon.
All my sides are equal.
All my angles are equal.
I have no centre of symmetry.
I have three axes of symmetry, and each of my angles is $60^\circ$.
Who am I?
ANSWER: EQUILATERAL TRIANGLE
EXPLANATION:
An equilateral triangle has 3 axes of symmetry and rotational symmetry of order 3.
A regular pentagon is also equilateral and equiangular with no centre of symmetry, but it has 5 axes.
2. RIDDLE:
I am a plane figure.
I am a polygon.
I have four sides.
My order of rotational symmetry is more than 1.
I have a centre of symmetry.
I have four axes of symmetry.
Who am I?
ANSWER: SQUARE
EXPLANATION:
A square has 4 axes of symmetry and rotational symmetry of order 4.
The rectangle, rhombus and parallelogram have order 2.
3. RIDDLE:
I am a plane figure.
I am a closed figure.
I have a centre of symmetry.
I have more than four axes of symmetry.
My order of rotational symmetry is at least 6.
I have infinitely many axes of symmetry: every line through my centre is one.
Who am I?
ANSWER: CIRCLE
EXPLANATION:
Every diameter of a circle is an axis of symmetry, and any rotation about the centre maps it onto itself.
The regular hexagon (6 axes) and regular octagon (8 axes) fit the other clues.
4. RIDDLE:
I am a plane figure.
I am a polygon.
I have four sides.
All my angles are equal.
I have a centre of symmetry.
My sides are not all equal, and I have exactly two axes of symmetry.
Who am I?
ANSWER: RECTANGLE
EXPLANATION:
A rectangle has 2 axes of symmetry (through the midpoints of opposite sides) and rotational symmetry of order 2.
The square fits the other clues but has 4 axes.
5. RIDDLE:
I am a plane figure.
I am a polygon.
I have four sides.
All my sides are equal.
I have a centre of symmetry.
My angles are not all equal, and my only axes of symmetry are my two diagonals.
Who am I?
ANSWER: RHOMBUS
EXPLANATION:
A rhombus has 2 axes of symmetry (its diagonals) and rotational symmetry of order 2.
The square fits the other clues, but its angles are all equal.
6. RIDDLE:
I am a plane figure.
I am a polygon.
I have four sides.
My order of rotational symmetry is 2.
I have a centre of symmetry.
I have no axis of symmetry at all.
Who am I?
ANSWER: PARALLELOGRAM
EXPLANATION:
A general parallelogram has rotational symmetry of order 2 but no axis of symmetry.
The rectangle and rhombus have order 2 as well, but each has 2 axes.