problem
How does your function grow?
Age
16 to 18
Challenge level
Compares the size of functions f(n) for large values of n.
problem
Climbing powers
Age
16 to 18
Challenge level
$2\wedge 3\wedge 4$ 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 $\sqrt{2}$?
problem
Big, bigger, biggest
Age
16 to 18
Challenge level
Which is the biggest and which the smallest of $2000^{2002}, 2001^{2001} \text{and } 2002^{2000}$?