Smallest positive integer
Puzzles$1^2+2^2=5$, which is not a square. $1^2+2^2+3^2=14$, which is not a square. What is the smallest positive integer value of [...]
Relationships between pentagonal and triangular numbers
Puzzles2016 is a triangular number. The first three triangular numbers are: 1, 3, 6. The first three pentagonal numbers are: [...]
Construct an equilateral triangle
PuzzlesConstruct an equilateral triangle with one vertex on each of three parallel lines using just a straight edge and a [...]
Smallest possible area for the triangle
PuzzlesThe points $A$ and $B$ are on the curve $y=x^2$ such that $AOB$ is a right angle. What points $A$ [...]
Split into two equal volumes
PuzzlesA cube is sliced vertically along the line shown in the diagram and the smaller part is thrown away. The [...]