ArchiveShow me a Random Puzzle
Most Recent Collections
Sunday Afternoon Maths LIXTurning Squares
Sunday Afternoon Maths LVIIIFactorial Pattern
Advent Calendar 2016
Sunday Afternoon Maths LVIILargest Odd Factors
List of All Puzzles
Tagstime geometry 2d shapes 3d shapes numbers spheres trigonometry complex numbers algebra lines graphs coordinates odd numbers fractions differentiation calculus folding tube maps ellipses triangle numbers money bases triangles squares area square numbers chess probability circles averages speed sport multiples dates factors parabolas functions logic cards games people maths shape prime numbers irreducible numbers probabilty angles proportion dice integration sum to infinity dodecagons hexagons multiplication factorials coins shapes regular shapes colouring grids floors integers rugby crosswords percentages digits sums rectangles clocks menace routes taxicab geometry remainders chalkdust crossnumber palindromes sequences means unit fractions division square roots surds doubling quadratics indices symmetry planes volume number partitions ave pascal's triangle mean advent arrows
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?
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?
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.
Source: Maths Jam
Prove that 1 and 9 are the only square numbers where all the digits are odd.
Triangles Between Squares
Prove that there are never more than two triangle numbers between two consecutive square numbers.
Source: Lewis Carroll's Games & Puzzles
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.