**Continue reading the story**"Convex cone"

## Monthly Archives for July, 2013

## Convex cone

This puzzle requires some knowledge of Linear Algebra.
Suppose are m non-zero column vectors in with non-negative entries. Assume the span of the m vectors is of dimension . Assume . Consider the convex cone
Show that we can find vectors in with positive entries such …

## Vigilance campaign

A city has M roads from north-south and N roads from east-west. The roads are small enough that the entire road is visible from any point on the road. The governor wants to monitor the roads, so he wishes to place policemen at intersections. What is the minimum number of policemen needed so that the entire road network is visible?
- via Math Puzzles

## Find fake coin

Four coins marked 1,2,3 and 5 respectively are given to you. The marks are supposed to be their weight, except that a fake coin weighs lighter than it should. There is one fake coin. Find it in 2 uses of the physical balance.
via Tanya Khovanova's blog