# Category: Puzzles

## Santa has 100 reindeer in 100 numbered stalls

### Relationships between pentagonal and triangular numbers

2016 is a triangular number. The first three triangular numbers are: 1, 3, 6. The first three pentagonal numbers are: [...]

### Construct an equilateral triangle

Construct 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

The 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

A cube is sliced vertically along the line shown in the diagram and the smaller part is thrown away. The [...]

### Sequence of perfect squares puzzle

Each 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

Given the list of the first n primes, 2, 3, 5,…, the product of the primes plus one will be [...]

### Common ratio and progressions puzzle

An 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

What would the shaded area of pattern 3 be? Reveal Solution The first shaded area is the area of the [...]

### Ways to complete the grid puzzle

I want to complete the cross figure shown here. I would like all eleven answers to be prime numbers and [...]

### Arrange seven points in a plane puzzle

Is it possible to arrange seven points in a plane so that any subset of three points will contain at [...]