Santa has 100 reindeer in 100 numbered stalls
PuzzlesSanta has 100 reindeer in 100 numbered stalls and 100 elves to boss about. He picks reindeer by the following [...]
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 [...]
Sequence of perfect squares puzzle
PuzzlesEach number in the sequence 49, 4489, 444889, 44448889 is a perfect square. (i.e. the first digits are always 4s, [...]
Given the list of n primes puzzle
PuzzlesGiven the list of the first n primes, 2, 3, 5,…, the product of the primes plus one will be [...]
Common ratio and progressions puzzle
PuzzlesAn arithmetic progression (AP) is a sequence of numbers with a common difference between them, e.g. 3, 7, 11, 15, [...]
Shaded area of pattern three
PuzzlesWhat would the shaded area of pattern 3 be? Reveal SolutionThe first shaded area is the area of the large [...]