![How Many Solutions?](/sites/default/files/styles/medium/public/thumbnails/content-00-11-15plus1-icon.jpg?itok=XUJ4oLm0)
Indices
![How Many Solutions?](/sites/default/files/styles/medium/public/thumbnails/content-00-11-15plus1-icon.jpg?itok=XUJ4oLm0)
![Climbing Powers](/sites/default/files/styles/medium/public/thumbnails/content-00-09-15plus1-icon.jpg?itok=pPouFKID)
problem
Climbing Powers
$2\wedge 3\wedge 4$ could be $(2^3)^4$ or $2^{(3^4)}$. Does it make any difference? For both definitions, which is bigger: $r\wedge r\wedge r\wedge r\dots$ where the powers of $r$ go on for ever, or $(r^r)^r$, where $r$ is $\sqrt{2}$?
![Growing](/sites/default/files/styles/medium/public/thumbnails/content-00-07-15plus1-icon.jpg?itok=Jry1mts7)
problem
Growing
Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)
![Telescoping series](/sites/default/files/styles/medium/public/thumbnails/content-99-05-15plus4-icon.jpg?itok=rGJaLA7y)
problem
Telescoping series
Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.
![More Mods](/sites/default/files/styles/medium/public/thumbnails/content-99-02-15plus1-icon.png?itok=yaNGKs9K)
![Card Shuffle](/sites/default/files/styles/medium/public/thumbnails/content-id-5402-icon.jpg?itok=SvWlagDK)
article
Card Shuffle
This article for students and teachers tries to think about how
long would it take someone to create every possible shuffle of a
pack of cards, with surprising results.
![Learn About Number Bases](/sites/default/files/styles/medium/public/thumbnails/content-00-03-art3-icon.jpg?itok=VbaEOR8z)
article
Learn About Number Bases
We are used to writing numbers in base ten, using 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Eg. 75 means 7 tens and five units. This article explains how numbers can be written in any number base.
![Modulus Arithmetic and a solution to Dirisibly Yours](/sites/default/files/styles/medium/public/thumbnails/content-99-01-art3-icon.jpg?itok=xlKXUfxw)
article
Modulus Arithmetic and a solution to Dirisibly Yours
Peter Zimmerman from Mill Hill County High School in Barnet, London
gives a neat proof that: 5^(2n+1) + 11^(2n+1) + 17^(2n+1) is
divisible by 33 for every non negative integer n.
![More Sums of Squares](/sites/default/files/styles/medium/public/thumbnails/content-99-01-art1-icon.jpg?itok=MvzvJazU)
![Sums of Squares and Sums of Cubes](/sites/default/files/styles/medium/public/thumbnails/content-98-12-art2-icon.jpg?itok=lpAZXn8O)
article
Sums of Squares and Sums of Cubes
An account of methods for finding whether or not a number can be written as the sum of two or more squares or as the sum of two or more cubes.