mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

9 December

The diagram below shows a rectangle. Two of its sides have been coloured blue. A red line has been drawn from two of its vertices to the midpoint of a side.
The total length of the blue lines is 50cm. The total length of the red lines is also 50cm. What is the area of the rectangle (in cm2)?

Show answer

20 December

The diagram to the right shows (two copies of) quadrilateral ABCD.
The sum of the angles ABC and BCD (green and blue in quadrilateral on the left) is 180°. The sum of the angles ABC and DAB (green and orange in quadrilateral on the left) is also 180°. In the diagram on the right, a point inside the quadrilateral has been used to draw two triangles.
The area of the quadrilateral is 850. What is the smallest that the total area of the two triangles could be?

Show answer

10 December

A line is tangent to a curve if the line touches the curve at exactly one point.
The line \(y=-160\,000\) is tangent to the parabola \(y=x^2-ax\). What is \(a\)?

Show answer

7 December

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

Show answer

20 December

What is the area of the largest area triangle that has one side of length 32 and one side of length 19?

Show answer

13 December

The diagram to the left shows three circles and two triangles. The three circles all meet at one point. The vertices of the smaller red triangle are at the centres of the circles. The lines connecting the vertices of the larger blue triangle to the point where all three circles meet are diameters of the three circles.
The area of the smaller red triangle is 226. What is the area of the larger blue triangle?

Show answer

7 December

The picture below shows eight regular decagons. In each decagon, a red triangle has been drawn with vertices at three of the vertices of the decagon.
The area of each decagon is 240. What is the total area of all the red triangles?

Show answer

19 December

The diagram to the right shows a triangle. Two of the sides of the triangle have been split into three pieces, with lines drawn from the opposite vertex. In total, the diagram now contains 27 triangles of any size.
Another triangle has two of its sides split into eight pieces, with lines drawn from the opposite vertex. How many triangles (of any size) would this create?

Show answer

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

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

Archive

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