Click here to win prizes by solving the puzzle Advent calendar.
Click here to win prizes by solving the puzzle Advent calendar.


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


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


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 2019,
puzzles about quadratics, or a random puzzle.


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


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


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