Given two billion distinct points on a plane such That no three are collinear. I color any half of them red and the Remaining blue. Is it always possible for you to join each red point to one (and Only one) blue point by means of line segments such that no two line segments Intersect?

Two concentric rings of uniform density at every point Are placed on a flat surface. Now since the centre of mass of a uniform Ring is its geometrical centre, the distance between the centers of Mass of the two rings are zero. Thus according to newtons law of Gravitation the attraction between themes (or at least tends to be) infinite, Making it impossible to pull one ring radially out from the other. However, as We know, this is not true. Why?

You have with you (1) a string of 1 meter length (2) 1 Kg weight (3) a watch. Now you want to find out the height of the Tallest tower -- say cn tower of toronto. How many ways can you devise to Measure it? They do not have to be practical, but scientifically Correct. Up to seven methods are child’s play.

For readers interested in pythagorean triplets with Consecutive natural numbers, take any odd number -- say 11 -- and square It. 11 squared = 121 = 2(60)+ 1. Add 60 squared to both sides to get 11 squared + 60 squared = 60 squared + 2(60) + 1 = (60 + 1) squared = 61 squared. What do we get? (11, 60, 61). Works every time. Prove it For a general case.

Find a nine-digit number which consists of all the Digits from 1 to 9 in which a number formed by first n digits is divisible By n where n is any number between 1 and 9. Maximum permissible trials are 4 after applying rules for divisibility by 2, 3, 4, 5, 6, and 8 for Elimination.

Here’s a puzzle my great grand-daddy told me in my Dreams. "son, when i was civil engineer there was once A great embarrassment. Once across two points in the City there was a huge traffic of people but no Direct road. They had to travel great lengths in order to reach Their destination.the governor ordered me to build a road across Those two points. It was completed in five years. But Horrors of horrors, as soon asteroid was built, it was No longer required! The very construction of

Ab is a line segment and p is any point in it, other than its centre. Using ruler only find a point q on ab extended such that ap / pb = aq / qb.

There is A one-way road one km long with two lanes, each lane five meters broad. Cars Cruise at 60 kmph on each lane. Distance between front bumpers of any two Successive cars is 10 meters which includes length of one car plus the clear Between the two cars. question (a): how many cars exit the road in one hour (your brilliant readers will find this childs play). then one morning mtnl digs a trench across one Lane at location half km of road length. The trench is 5m x 5m which makes a Single lane

Take a lighted agarbatti (joss stick) and make sure of two Things: (1) the stream of smoke is clearly visible and (2) there is no Draught to disturb it. Now give gentle tugs of the wrist. At a certain Optimal amount of such tugging you can see rings of smoke forming in the Emanating chaotic smoke stream. I dont know if this is a known phenomenon or Not. If not, let the rings be known as owaiss rings. The question is, What causes these rings?

Which is the smallest integer-sided square that is Inscribed in a integer-sided right triangle so that one side of the Square lies on the hypotenuse?