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Proof 2 = 1

Classic fallacies

Can you figure out misstep in above?

Here it is figured out! 

How Proof : 2 = 1 is Wrong


What was allowed?

Since a = b, then a - b = 0.

So we can't divide both sides by (a - b) on both sides to eliminate (a -b) since division by 0 is not defined or infinity!


Classic Fallacies, false algebra, dirty maths tricks,

Non-Zero Number Using Only Zeros


The challenge is bringing 120 on other side of = using only 0 s. You are not allowed to use any number from 1 to 9 but allowed to use +, -, x, / .However you can use any number of zeros!

Making RHS non zero using zeros at LHS
How it could be?


Challenge accepted here! 

Non-Zero Output Using Zero Input


What was the challenge?

All you need to use ! here like below.

(0! + 0! + 0! + 0! + 0!)! = 120.

Non zero RHS using zeros at LHS

Unfair Loss in Savings of Life

On his 20th birthday, Ajay started depositing Rs.500 in his saving box. His brother Vijay used to withdraw Rs.100 from the same box on his birthday every year. On his 60th  birthday, Ajay opens his box & finds only Rs.1000 in it.

How this could be possible?

Two brothers at old age
Ajay & Vijay

Having Birthday On Leap Day


Since Ajay celebrates his birthday on 29th February, he used to deposit Rs.500 in saving box once in 4 years. From age 20 to 60, he celebrated only 10 birthdays saving only 500 x 10 = 5000. 

But Vijay withdrawing Rs.100 every year means he took 100 x 40 = 4000 so far.
That's why only 5000 - 4000 = 1000 left in the box.

Leap Day birthday affecting life savings

Just To Test Your Common Sense

Below are four (4) questions and a bonus question. You have to answer them instantly. You can't take your time, answer all of them immediately. Okay?
  
Let's find out just how clever you really are .
 
Ready?
GO!!! 

Question 1 :
You are participating in a race. You overtake the second person. What position are you in?


Question 2 :
If you overtake the last person, then you are...?


Question 3 :
Very tricky math! Note: This must be done in your head only. Do NOT use paper and pencil or a calculator. Try it.
   
Question 4 :
Mary's father has five daughters: 1. Tana, 2. Tene, 3. Tini, 4. Tono. What is the name of the fifth daughter? 


Bonus Question :
There is a mute person who wants to buy a toothbrush. By imitating the action of brushing one's teeth he successfully expresses himself to the shopkeeper and the purchase is done.
Now if there is a blind man who wishes to buy a pair of sunglasses, how should he express himself?

How good is your common sense?

View your results here! 

 

Verify Answers of Common Sense Test


Here is the TEST! 

Answer 1: If you answered that you are first, then you are absolutely wrong! If you overtake the second person and you take his place, you are second!
 

Answer 2: If you answered that you are second to last, then you are wrong again. Tell me, how can you overtake the LAST person!
 

Answer 3: Did you get 5000? The correct answer is actually 4100.
Don't believe it? Check with your calculator! Today is definitely not your day. Maybe you will get the last question right?

Answer 4: Tunu?
NO! Of course not. Her name is Mary. Read the question again.


Verifiy answers of common sense test

Bonus Answer : He just has to open his mouth and ask, so simple

'Sabrina and Samantha' Brain Teaser

Sabrina gave Samantha as many dollars as Samantha started out with. Samantha then gave Sabrina back as much as Sabrina had left. Sabrina then gave Samantha as back as many dollars as Samantha had left, which left Sabrina broke and gave Samantha a total of $80.00. 

How much did Sabrina and Samantha have at the beginning of their exchange?

How much  'Sabrina and Samantha' had?

Initial Amount Sabrina & Samantha had


But what was that? 

This could be solved using simultaneous equations but going in reverse makes it easy.

At each stage, one's money is doubled. At last stage, Samantha doubled money to 80 by receiving 40 from Sabrina. So both had 40 before that.

How Sabrina had 40? Since Samantha gave her 20 at previous transaction. So Samantha had 40+20=60 & Sabrina had 20 before this transfer. 

And how Samantha had 60? Since she received 30 from Sabrina at previous transfer. So Sabrina had 30+20=50 & Samantha had 30 before the transfer.

Hence at start , Sabrina had 50 & Samantha had 30!



Initially Sabrina had 50 & Samantha had 30!

Probability of Correct Package Labeling

Brad Doe works for a packaging company. One day, he received four separate orders and accidentally mixed up the addresses, so he applied the
address labels at random. 

What is the probability that exactly three packages were correctly labeled?

Probability of correct package labels
Labeled Packages


 Skip to answer! 

Common Sense in Finding Probability


Answer is 1!

If three are correctly placed fourth has to be. There are only 4!

Not probability but common sense

Would You Help This Farmer ?

A farmer had 25 cows. To identify easily he numbered them from 1 to 25. Interestingly, each cow produces liters of milk equal to the respective number given. For example, a cow numbered 5 gives 5 liters of milk or a cow numbered 18 produces 18 liters of milk. Now that farmer had 5 sons. Farmer wants to share those 25 cows among his 5 sons with each son getting 5 cows. But he wants to make sure each son would get equal amount of milk.

How should he make 5 groups of cows to distribute among his sons?


Group 25 special cows in 5 groups
Please, Help me!


This is what farmer need to do! 

Fair Distribution of Farmer's Cows


What was the interesting?

First let's name 5 sons as A,B,C,D & E. Now look at the image below.

Just collect numbers surrounded by same shapes. If you observe carefully answer, a difference of 4 created at one place which is compensated at other 4. Each son would be getting 65 liters of milk.


Fair Distribution of 25 cows among 5 sons
Fair Distribution of Cows

Man Walking on Moving Escalator

 A man can walk up a moving "up" escalator in 30 seconds. He can walk down this moving "up" escalator in 1-1/2 minutes. If his walking pace is the same going upstairs as downstairs, how long would it take him to climb the escalator if it was stationary? How long would it take him to go up the moving escalator if he stood still?


Man walking up & down on moving escalator


Calculated here! 

Man on Stationary Escalator


What was asked to calculate? 

Let L = length of stair , M = Man's speed & E = Elevator's speed.

Let's remind what we have learned in our school days.

Speed = Distance/Time

i.e.

Distance = Speed  x  Time

While moving 'up' along with upward moving elevator, 

30(M+E) = L     ......(1)

While moving 'down' against 'upward' moving elevator, man's speed has to be faster than elevator's speed so that he can reach down at the stair. Otherwise he would never reach down always falling short.

90(M-E) = L    .......(2)

From (1) & (2), we get,

30M+30E=90M-90E
60M=120E
M=2E     .....(3)
E=M/2    .....(4)
Putting (3) in (1),
45M=L
M=L/45    
(Speed=Distance/Time)

Hence man alone needs 45 seconds to climb up that stationary elevator.


Man climbing up on stationary escalator
Stationary Escalator

Putting (4) in (1), gives,

E=L/90
(Speed=Distance/Time)

So elevator needs 90 seconds to push standing man up.

Solve this Murder case (challenge)

Solve this Murder case (challenge)..

Near Mumbai

A man was found murdered on 9-11-2016 Wednesday afternoon at 12.35 PM in his house...... His wife called police at 3:23 PM.

Police questioned everyone..

Wife: I was sleeping..

Son: I went for movies with my gf

Neighbor: We went for the marriage..

Driver: I went to ATM withdraw cash..

Cook: I went to Wine shop to buy Wine..

Gardener: I was in garden the whole time. I didn't hear anything.
.
Watch Man: I went to my relative's Marriage..


Catch the Murderer

Police arrested the murderer immediately..
Who was it? 

Find who was that here! 

Murder Mystery Investigation


But what was the case? 

Driver was the murderer!

He must be lying as ATMs were closed on 9-11-2016 after note demonetization in India.


Murderer in the murder case
 

Just A Spare Thought...


I always had this concept in my mind but absolutely no idea whether it's possible or not.

We know, light takes 8 minutes 20 seconds to travel from Earth to Sun. So if we are looking at Sun at any time it's 8 minutes 20 seconds old. Now if we place a very high power camera with a great optical zoom at few light years say 10 years from Earth & zoom at Earth then wouldn't it possible to observe what was going on Earth 10 years ago? Wouldn't it be a time machine only difference it's not taking us physically at that time.


Launching camera light years ahead


I know it would be literally impossible to place such camera but who had thought communications without wires few centuries ago! Just a crazy thought shared.

Make Dog To Look In Opposite

Challenge here is that you need to make dog to look at opposite direction by just moving only 2 match sticks.

Make it look in opposite direction




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