22 December

What is the largest number which cannot be written as the sum of distinct squares?

Products and sums of squares

Show that the product of any two numbers, each of which is the sum of two square integers, is itself the sum of two square integers.

Show answer & extension

Odd squares

Source: Maths Jam
Prove that 1 and 9 are the only square numbers where all the digits are odd.

Show answer & extension

Triangles between squares

Prove that there are never more than two triangle numbers between two consecutive square numbers.

Show answer & extension

Square numbers

Towards the end of his life, Lewis Carroll recorded in his diary that he had discovered that double the sum of two square numbers could always be written as the sum of two square numbers. For example
$$2(3^2 +4^2 )=1^2 +7^2$$ $$2(5^2 +8^2 )=3^2 +13^2$$
Prove that this can be done for any two square numbers.

Show answer & extension

Chessboard squares

It was once claimed that there are 204 squares on a chessboard. Can you justify this claim?

Show answer & extension


Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020