MathDB

2

Part of 2001 Pan African

Problems(2)

Child builds a wall

Source: Pan African 2001

10/4/2005
Let nn be a positive integer. A child builds a wall along a line with nn identical cubes. He lays the first cube on the line and at each subsequent step, he lays the next cube either on the ground or on the top of another cube, so that it has a common face with the previous one. How many such distinct walls exist?
geometry3D geometrygeometric transformationreflectionfloor function
Sum of [x]

Source: Pan African 2001

10/4/2005
Find the value of the sum: ∑i=12001[i] \sum_{i=1}^{2001} [\sqrt{i}] where [x][ {x} ] denotes the greatest integer which does not exceed xx.