MathDB

1

Part of 2000 IMC

Problems(2)

A fixed point

Source: IMC 2000, Day 1, Problem 1

10/14/2005
Does every monotone increasing function f:[0,1]→[0,1]f : \mathbb[0,1] \rightarrow \mathbb[0,1] have a fixed point? What about every monotone decreasing function?
functionreal analysis
Dividing a square

Source: IMC 2000 Day 2 Problem 1

10/27/2020
Show that a square may be partitioned into nn smaller squares for sufficiently large nn. Show that for some constant N(d)N(d), a dd-dimensional cube can be partitioned into nn smaller cubes if n≥N(d)n \geq N(d) .