mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

23 December

There are 18 ways to split a 3 by 3 square into 3 rectangles whose sides all have integer length:
How many ways are there to split a 10 by 10 square into 3 rectangles whose sides all have integer length?

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

19 December

The diagram below shows three squares and five circles. The four smaller circles are all the same size, and the red square's vertices are the centres of these circles.
The area of the blue square is 14 units. What is the area of the red square?

Show answer

Is it equilateral?

In the diagram below, \(ABDC\) is a square. Angles \(ACE\) and \(BDE\) are both 75°.
Is triangle \(ABE\) equilateral? Why/why not?

Show answer

16 December

There are 204 squares (of any size) in an 8×8 grid of squares. Today's number is the number of rectangles (of any size) in a 2×19 grid of squares

14 December

There are 204 squares (of any size) in an 8×8 grid of squares. Today's number is the number of squares in a 13×13 grid of squares

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

Square deal

This unit square is divided into four regions by a diagonal and a line that connects a vertex to the midpoint of an opposite side. What are the areas of the four regions?

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

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

Archive

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