ArchiveShow me a Random Puzzle
Most Recent Collections
Sunday Afternoon Maths LXIXYZ
Sunday Afternoon Maths LXWhere is Evariste?
Bending a Straw
Sunday Afternoon Maths LIXTurning Squares
List of All Puzzles
Tagstime geometry 2d shapes 3d shapes numbers spheres trigonometry complex numbers algebra lines graphs coordinates odd numbers fractions differentiation calculus folding tube maps ellipses triangle numbers money bases triangles squares area square numbers chess probability circles averages speed sport multiples dates factors parabolas functions logic cards games people maths shape prime numbers irreducible numbers probabilty angles proportion dice integration sum to infinity dodecagons hexagons multiplication factorials coins shapes regular shapes colouring grids floors integers rugby crosswords percentages digits sums rectangles clocks menace routes taxicab geometry remainders chalkdust crossnumber palindromes sequences means unit fractions division square roots surds doubling quadratics indices symmetry planes volume number partitions ave pascal's triangle mean advent arrows addition
Bending a Straw
Two points along a drinking straw are picked at random. The straw is then bent at these points. What is the probability that the two ends meet up to make a triangle?
Two players take turns placing identical plates on a square table. The player who is first to be unable to place a plate loses. Which player wins?
Earlier this year, I wrote a blog post about different ways to prove Pythagoras' theorem. Today's puzzle uses Pythagoras' theorem.
Start with a line of length 2. Draw a line of length 17 perpendicular to it. Connect the ends to make a right-angled triangle. The length of the hypotenuse of this triangle will be a non-integer.
Draw a line of length 17 perpendicular to the hypotenuse and make another right-angled triangle. Again the new hypotenuse will have a non-integer length. Repeat this until you get a hypotenuse of integer length. What is the length of this hypotenuse?
The number of degrees in one internal angle of a regular polygon with 360 sides.
What is the volume of the smallest cube inside which a rectangular-based pyramid of volume 266 will fit?
What is the maximum number of lines that can be formed by the intersection of 30 planes?
Cross Diagonal Cover Problem
Source: Gaurish Korpal
Draw with an \(m\times n\) rectangle, split into unit squares. Starting in the top left corner, move at 45° across the rectangle. When you reach the side, bounce off. Continue until you reach another corner of the rectangle:
How many squares will be coloured in when the process ends?
The diagram shows two semicircles.
\(CD\) is a chord of the larger circle and is parallel to \(AB\). The length of \(CD\) is 8m. What is the area of the shaded region (in terms of \(\pi\))?