# Puzzles

## Archive

Show me a random puzzle**Most recent collections**

#### Sunday Afternoon Maths LXVII

Coloured weightsNot Roman numerals

#### Advent calendar 2018

#### Sunday Afternoon Maths LXVI

Cryptic crossnumber #2#### Sunday Afternoon Maths LXV

Cryptic crossnumber #1Breaking Chocolate

Square and cube endings

List of all puzzles

## Tags

partitions percentages logic money symmetry rectangles chocolate square numbers doubling multiplication division indices 3d shapes routes perimeter crosswords factors bases regular shapes squares cube numbers algebra sum to infinity remainders digits integration square roots arrows palindromes coordinates fractions differentiation 2d shapes graphs factorials number angles taxicab geometry sums chess numbers ellipses menace parabolas mean addition polygons unit fractions spheres pascal's triangle means speed cryptic crossnumbers clocks cryptic clues proportion dice advent crossnumbers circles books complex numbers ave cards lines time chalkdust crossnumber functions dodecagons perfect numbers quadratics area triangles surds calculus colouring hexagons balancing sport irreducible numbers rugby shape geometry scales planes volume probabilty multiples wordplay folding tube maps star numbers christmas sequences floors dates integers averages prime numbers shapes people maths coins trigonometry odd numbers grids probability triangle numbers games## 11 December

This puzzle is inspired by a puzzle Woody showed me at MathsJam.

Today's number is the number \(n\) such that $$\frac{216!\times215!\times214!\times...\times1!}{n!}$$ is a square number.

## Square and cube endings

Source: UKMT 2011 Senior Kangaroo

How many positive two-digit numbers are there whose square and cube both end in the same digit?

## 16 December

There are 204 squares (of any size) in an 8×8 grid of squares. Today's number is the number of rectangles (of any size) in a 2×19 grid of squares

## 14 December

There are 204 squares (of any size) in an 8×8 grid of squares. Today's number is the number of squares in a 13×13 grid of squares

## What's the star?

In the Christmas tree below, the rectangle, baubles, and the star at the top each contain a number. The square baubles contain square numbers; the triangle baubles contain triangle numbers; and the cube bauble contains a cube number.

The numbers in the rectangles (and the star) are equal to the sum of the numbers below them. For example, if the following numbers are filled in:

then you can deduce the following:

What is the number in the star at the top of this tree?

*You can download a printable pdf of this puzzle here.*

## Square pairs

Source: Maths Jam

Can you order the integers 1 to 16 so that every pair of adjacent numbers adds to a square number?

For which other numbers \(n\) is it possible to order the integers 1 to \(n\) in such a way?

## Square factorials

Source: Woody at Maths Jam

Multiply together the first 100 factorials:

$$1!\times2!\times3!\times...\times100!$$
Find a number, \(n\), such that dividing this product by \(n!\) produces a square number.

## Lots of ones

Is any of the numbers 11, 111, 1111, 11111, ... a square number?