The Distance Unlocked

What was the question?

Just count Vowels V & Consonants C in any 2 spelling to get how much they value.


From BERLIN,

2V + 4C = 200

V + 2C = 100             ........(1)

From ROME,

2V + 2C = 400

V + C = 200               .......(2)

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

V = 300 & C = -100

For CARDIFF, we have,


2V + 6C = 100. 

So CARDIFF = 100 miles

Wrong Address By Liar

Mr. House would like to visit his old friend Mr. Street, who is living in the main street of a small village. The main street has 50 houses divided into two blocks and numbered from 1 to 20 and 21 to 50. Since Mr. House has forgotten the number, he asks it from a passer-by, who replies "Just try to guess it." Mr. House likes playing games and asks three questions:

1. In which block is it?

2. Is the number even?

3. Is it a square?

After Mr. House has received the answers, he says: "I'm still doubting, but if you'll tell me whether the digit 4 is in the number, I will know the answer!". Then Mr. House runs to the building in which he thinks his friend is living. He rings, a man opens the door and it turns out that he's wrong. The man starts laughing and tells Mr. House: "Your advisor is the biggest liar of the whole village. He never speaks the truth!". Mr. House thinks for a moment and says "Thanks, now I know the real address of Mr. Street".

 
What is the address of Mr. Street?

This is how Mr.House found correct address! 

Source 

Correct Address Identified !

How pointed towards the wrong one? 

Since Mr. House was able to run at one house after answers of passer-by, he must have got clear clues from that.

3. Is it square ?
  
First thing is sure that, the number must not be a non-square otherwise Mr.House wouldn't be sure as there are plenty of non-square numbers between 1 to 50. So it must be either 4,9,16,25,36,49. (1 is omitted for a reason)

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1. In which block is it?

Two possible answers here & 2 possible conclusions.

Block 1  :  4,9,16

Block 2  :  25,36,49

------------------------------------------------------------------------------------------

2. Is the number even ?

Now had passer-by  answered Block 1 in 1st question & odd now then Mr. House would have come to know one exact number 9 (that's why 1 omitted here).

Or had he answered Block 2 in 1st question & even now then also Mr. House would have 1 number i.e. 36.

So in both cases, Mr. House would have got 1 fixed number with no point in asking extra question.


That means the passer-by must have told following answers & their possible conclusions are-

Block 1  :  Even  :  Square  :  4,16

Block 2  :  Odd   :  Square  :  25,49

Connect Dots with Straight Lines

Can you connect all nine dots with only four straight lines without losing contact with the paper while drawing? 

Read here how it can be done!

Source 
 

Connected Dots With Straight Lines

What was the challenge? 

This question often asked in personality development training courses. It needs some out of box thinking. In the question, no where it is mentioned that you line can't go beyond 3 dots. But our brain assumes that & try to find the solution according to that only!

The Alphamatic Problem

In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent different digits.

   ABCABA 

+

   BBDCAA 

+

   ABEABB 

+ 

   ABDBAA

-------------------

 AAFGBDH

What does the complete addition look like in digits? 

Note : Alphamatic in the title is word derived from Alphabets & Mathematics. In such problems numbers are replaced by alphabets. The challenge is to find the number for each alphabet satisfying given mathematics equation.

Step by step answer is here! 

Source 

Answer Of Alphamatic Problem

Here is question!

 First of all let's write down the equation once again.


   ABCABA 

+

   BBDCAA 

+

   ABEABB 

+ 

   ABDBAA

-------------------

 AAFGBDH

We will refer to places in number from left as a first, second, third...sixth instead of tenth, hundredth, thousandth etc. 

First we need to find if the 5 digits of first number itself i.e. ABCAB are carries forwarded from previous place.  

From the addition of variable from first place, we get,

3A + B  = 10A + A ........(1)

B  =  8A              ........(2)

Only numbers satisfying above are A = 1 & B = 8 , but at previous place we have addition of 4 B's. If B = 8, then addition at second place would be 32 with F = 2 & carry 3 which is not equal to A = 1. So A can't be a carry. So we need to modify (2) above as

B + x = 8A .........(2)....Where 'x' is carry forwarded from second place.

If B = 1 or 2 then x = 0 as  at second place we would have F = 4 or 8. In that case, A would be fractional. Some other possible combinations for B, A & x are,

B = 9, x = 3,   8A = 12,

B = 8, x = 3,   8A = 10,

B = 7, x = 2,   8A =  9,

B = 6, x = 2,   8A = 8,

This is the only combination that can make A a whole number. So A = 1, B = 6.

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From sixth place, we have,

H = 3A + B = 9

---------------------------------------------------------------------------------------------

From fifth place, we have,

D = 2A + 2B  = 14

But it has to be single digit i.e. D = 4 with 1 carry forwarded to next.

---------------------------------------------------------------------------------------------

From fourth place,

B = 2A + B + C + 1  .....1 is carry from last place.

6 = 9 + C

Now C can't be negative hence C + 9 has to be 2 digit number with 6 at last digit.Since addition of 2 single digit numbers never exceeds 18, C + 9 has to be 16.

16 = 9 + C 

gives, C = 7 & carry 1 forwarded to third place.

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Nightclub Tragedy

An American nightclub called 'The Coconut Grove' had a terrible fire in which over 400 people died. A simple design flaw in the building led to the death toll being so high. Subsequently, regulations were changed to ensure that all public buildings throughout the country eliminated this one detail which proved so deadly.

What was it?


Get here to know what was that! 

Source 

Change In Regulations After Tragedy

What was the tragedy? 

This is based on a true story:

The doors at the Coconut Grove opened inward. In the mad dash to escape the fire, people were crushed against the doors and couldn't pull them open. After the Coconut Grove disaster in 1942, all public buildings had to have doors which opened outward.

Loss Due To Fake Currency Note?

A lady buys goods worth Rs. 200 from a shop. (shopkeeper is selling the goods with zero profit). The lady gives him Rs. 1000 note. The shopkeeper gets the change from the next shop and keeps Rs. 200 for himself and returns Rs. 800 to the lady. Later the shopkeeper of the next shop comes with the Rs. 1000 note saying "duplicate" and takes his money back.
 
How much LOSS did the shopkeeper face?

Find that LOSS here!

Source 

'Cashless' Transaction

What was the tricky? 

The shopkeeper's getting change for Rs.1000 from the next shop is just to confuse you.
He brought Rs.1000 from that shop & gave back Rs.1000. There is no loss or profit from that end. Now he gave genuine Rs.800 & product of Rs.200 to the lady. In return, he got Rs.0 as the Rs.1000 note offered by the lady was fake one. So total loss the shopkeeper faced is of Rs.1000. 

 

Same Issue Different Approaches

Two newly launched firms started manufacturing soaps in their production unit. After few day, both started facing the same issue. Few soap wrappers were remaining empty without soaps within those. Both manufacturers asked their employees to find solution on this. Employees of one firm did lot of research & developed a machine to detect the empty wrappers. For that they invested lot of time & money. While employees of competitor were smart & just brought one thing from the market & solved the problem.
What was that thing? 

Know here what did they bring? 

The Most Efficient Approach Matters

What was the issue? 

The employees of other firm were smart. They just brought table fan from the market. Now they put it in front of chain where soaps with wrappers are placed & moved for the packaging at last stage of production. Air flowing from fan started flowing away empty wrappers off the chain. In this way, they invented smart way to detect the empty wrappers. A simple solution that saved a lot of money & time! 

"Make The Line Shorter!"

Once a teacher asked student the question that Akbar once has asked to Birbal. Teacher drawn a line on a paper with pencil & posted paper on a board. He asked students to make the line shorter without erasing by eraser or extending it with pencil.

One of the student who knew that story of Akbar - Birbal came & just draws another bigger line ahead of previous line. Now the other line looked shorter.

   
Now teacher decides to trick the students. 'Now without touching any line it make left line longer & right line shorter', he asks further.

The student was smart & just rotated the paper upside down. That way, now left line looked longer & right one shorter!

Complex Time, Speed & Distance Maths

There is a circular race-track of diameter 1 km. Two cars A and B are standing on the track diametrically opposite to each other. They are both facing in the clockwise direction. At t=0, both cars start moving at a constant acceleration of 0.1 m/s/s (initial velocity zero). Since both of them are moving at same speed and acceleration and clockwise direction, they will always remain diametrically opposite to each other throughout their motion.

At the center of the race-track there is a bug. At t=0, the bug starts to fly towards car A. When it reaches car A, it turn around and starts moving towards car B. When it reaches B, it again turns back and starts moving towards car A. It keeps repeating the entire cycle. The speed of the bug is 1 m/s throughout.

After 1 hour, all 3 bodies stop moving. What is the total distance traveled by the bug?

Find out complex calculations here!

Simple Solution of Complex Problem

Here is that complex looking problem! 

Everything built, written or designed in the given problem is to distract you from basic physics formula.

Speed = Distance / Time

Hence,

Distance = Speed x Time 

All the details given except speed of bug & time for which it traveled are there to confuse you. Speed of bug is 1 m/s & it traveled for 1 hour = 3600 seconds.

Distance = 1 x 3600 = 3600 m

So the total distance traveled by the bug is 3600 m.

 

What was the neighbor's solution?

An old farmer died and left 17 cows to his three sons. In his will, the farmer stated that his oldest son should get 1/2, his middle son should get 1/3, and his youngest son should get 1/9 of all the cows. The sons, who did not want to end up with half cows, sat for days trying to figure out how many cows each of them should get.

One day, their neighbor came by to see how they were doing after their father's death. The three sons told him their problem. After thinking for a while, the neighbor said: "I'll be right back!" He went away, and when he came back, the three sons could divide the cows according to their father's will, and in such a way, that each of them got a whole number of cows.

What was the neighbor's solution? 

Here is that solution! 

Source

Neighbor's Solution on Old Farmer's Will

What was the problem with the will?

Neighbor went & brought a extra cow. Now there were 18 cows. The oldest son got 
1/2 x 18 = 9 cows, middle son got 1/3 x 18 = 6 cows and youngest son got 1/9 x 18 = 2 cows. In this way, total 9 + 6 + 2 = 17 cows distributed among 3 sons but left with 1 cow which neighbor took with himself. 

Do Not Tap on the Glass

A man works at an aquarium. Every day he spends a large chunk of his time trying to stop people from tapping on the glass at the shark tank. Finally, fed up with it, he comes up with a solution. The solution works perfectly, the next day no one taps on the glass. However, he is fired for it. 

What was the man’s solution?

Read here that solution! 

Source 

'Reward' For 'Creative' Solution

But what made to use some creativity? 

The man did just a little trick. He painted a crack on the glass. Now people visiting stopped tapping on the glass with fear that it would break. But in that attempt man made the aquarium to look terrible & unsafe! Hence fired!