Eliminating Square in 40 Matchsticks Challenge!

What was the challenge?

All that we need to do is that remove these differently colored 9 matchsticks.

So we get, 

There can be other variations of this answer but we have to remove 9 matchsticks at least to make sure there is no square.

Who Will Win the Race? You or I ?

Here’s a long corridor with a moving walkway. Let’s race to the far end and back. We’ll both run at the same speed, but you run on the floor and I’ll run on the walkway, going “downstream” to the far end and “upstream” back to this point. 

Who will win?

This person will be the winner of the race!

"You Will Be Winner of the Race!"

How race was conducted?

Let's assume that we have to run 60 units forward & 60 units backward i.e. total 120 units of distance.

Let 10 units be the speed of the moving walkway. Then I have to run faster than 10 while coming back "upstream" to reach at the source again.

So let 20 units be the our speed of running.

Speed = Distance/Time

Time = Distance/Speed

Time that you need to complete the race = 120/20 = 6 unit.

Time that I need to go forward = 60/(20+10) = 2 units.

Time that I need to come back = 60/(20-10) = 6 units.

Hence, 

Time that I need to complete the race = 4 + 12 = 8 units.

I will require more time to complete the race, that's why you will be the winner of the race!  

Interesting Fact of Handshake Count

Suppose we fill Yankee Stadium with 50,000 people and ask them to spend the day shaking hands with one another.

Prove that, at the end of the day, at least two participants will have shaken hands with the same number of people.

Click here for proof!

Proving Interesting Fact of Handshake Count

What was that fact?

Let's contradict the given fact & assume no 2 people have same number of handshakes. In that case, the most gregarious person would have 49999 handshakes & next gregarious person would shake hands with 49998 people and so on. 

This way, the shyest person should have 0 shake hands. But the most gregarious guy must have had handshake with this shyest guy as his count of 49999 also includes this shyest guy. So this is impossible case.

Hence, at least 2 participants would have shaken hands with the same number of people.

 
In other way, the most shyest participant would have 1 handshake, next shyer guy would have 2 & so on. The more gregarious would have 49999 handshakes that includes the shake hand with the most gregarious person. Now, most gregarious person is bound to have 49999 handshakes as he/she can't have 50000 as there are only 50000 people in the stadium including himself/herself. 

That's why, at least 2 participants would have shaken hands with the same number of people.

How Far Did I Run?

I leave my front door, run on a level road for some distance, then run to the top of a hill and return home by the same route. I run 8 mph on level ground, 6 mph uphill, and 12 mph downhill. 

If my total trip took 2 hours, how far did I run?

I ran the distance.....Click here for more!

Calculation of Avarage Speed is Tricky!

First read what was the question!

Let's first find my average speed when I was running uphill & downhill.

Assume 'x' be the distance that I have to run to reach at the top of the hill in time 'y'.

So x/y = 6 mph.

While running downhill, I cover same distance 'x' in time 'y/2' as I ran at double speed of 12 mph.

Average speed = Total Distance / Total Time

Average speed = (x + x) / (y + y/2)

Average speed = (4/3)(x/y)

Average speed = (4/3) x 6

Average speed = 8 mph.

That means my average speed on hill is equal to the my speed on level ground and that is 8 mph.

Since I ran for 2 hours in my trip the distance I ran is 8 x 2 = 16 miles.