mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

7 December

What is the area of the largest triangle that fits inside a regular hexagon with area 952?

Show answer

5 December

How many different isosceles triangles are there whose perimeter is 50 units, and whose area is an integer number of square-units?
(Two triangles that are rotations, reflections and translations of each other are counted as the same triangle. Triangles with an area of 0 should not be counted.)

Show answer

12 December

The diagram to the left shows a large black square. Inside this square, two red squares have been drawn. (The sides of the red squares are parallel to the sides of the black square; each red square shares a vertex with the black square; and the two red squares share a vertex.) A blue quadrilateral has then been drawn with vertices at two corners of the black square and the centres of the red squares.
The area of the blue quadrilateral is 167. What is the area of the black square?

Show answer

2 December

Carol draws a square with area 62. She then draws the smallest possible circle that this square is contained inside. Next, she draws the smallest possible square that her circle is contained inside. What is the area of her second square?

Show answer

23 December

Today's number is the area of the largest area rectangle with perimeter 46 and whose sides are all integer length.

Show answer

2 December

Today's number is the area of the largest dodecagon that it's possible to fit inside a circle with area \(\displaystyle\frac{172\pi}3\).

Show answer

Squared circle

Each side of a square has a circle drawn on it as diameter. The square is also inscribed in a fifth circle as shown.
Find the ratio of the total area of the shaded crescents to the area of the square.

Show answer

Two triangles

Source: Maths Jam
The three sides of this triangle have been split into three equal parts and three lines have been added.
What is the area of the smaller blue triangle as a fraction of the area of the original large triangle?

Show answer & extension

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

spheres scales dice dates tangents addition floors sport irreducible numbers colouring gerrymandering symmetry geometric mean polygons cryptic crossnumbers division perfect numbers balancing combinatorics pentagons triangle numbers tournaments coordinates circles folding tube maps dodecagons chess probability proportion people maths chocolate sum to infinity albgebra squares expansions percentages chalkdust crossnumber range determinants square numbers regular shapes rugby the only crossnumber ave cryptic clues probabilty lines differentiation odd numbers decahedra menace grids triangles factorials remainders partitions tiling pascal's triangle games even numbers geometry functions factors digital clocks cube numbers ellipses geometric means integers dominos consecutive integers sets arrows averages speed perimeter advent bases sums doubling volume books complex numbers graphs numbers christmas shape square roots fractions algebra polynomials prime numbers median unit fractions mean integration quadratics area rectangles consecutive numbers crossnumber binary matrices crossnumbers hexagons axes star numbers planes digital products parabolas taxicab geometry calculus coins multiples trigonometry surds 2d shapes 3d shapes crosswords quadrilaterals digits routes cubics multiplication elections number palindromes cards money sequences products angles shapes wordplay means time logic clocks indices

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024