mscroggs.co.uk
mscroggs.co.uk

subscribe

Sunday Afternoon Maths XVII

 Posted on 2014-06-15 

Differentiate this

$$f(x)=e^{x^{ \frac{\ln{\left(\ln{x}\right)}}{ \ln{x}}} }$$
Find \(f'(x)\).

Show answer

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

N

Consider three-digit integers \(N\) such that:
(a) \(N\) is not exactly divisible by 2, 3 or 5.
(b) No digit of \(N\) is exactly divisible by 2, 3 or 5.
How many such integers \(N\) are there?

Show answer & extension

MathsJam

Maths Jam is always held on the second-to-last Tuesday of the month. This month, it will be held on the 17th. What is the earliest date in the month on which Maths Jam can fall and when will this next happen?

Show answer & extension

Tags: dates
If you enjoyed these puzzles, check out Advent calendar 2024,
puzzles about people maths, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2025