Spirit Of Genius

Suppose there are twin brothers; one which always tells the truth and one which always lies. What single yes/no question could you ask to either brother to figure out which one is which? (Condition is you can't ask question whose answer you already know. e.g. does earth rotate around the sun?)

How to identify liar/truth teller among twins?

This should be that question!

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Question To Identify Liar/Truth Teller

First know about twins.

We should ask one question,

"Would your brother say that you tell the truth?"

Now if the question is asked the truth teller, then he knows his liar brother would say NO to this question. Hence he would say NO straightaway.

And if the question being asked to liar then he knows that his brother is going to say NO to this question but as a liar he would lie once again & would say YES to the question asked.

So depending on what reply we get, we can easily identify the liar & truth teller brother.

Reply distinguishing liar from truth teller

Remove Matches To Match Number

Remove six matches to make 10.

Shown here how it can be done!

Matches To Match Number

What was the challenge?

It's pretty simple one. Nowhere it is mentioned that you have to make it as

10 & not allowed to make TEN. So three sticks from first, one from second &

2 from third gives us TEN.

However, we can make it as 10 as well. Removing 1 stick from first, 4 from

second & 1 from third produces 10.

The True Statement?

A. The number of false statements here is one.

B. The number of false statements here is two.

C. The number of false statements here is three.

D. The number of false statements here is four.

Which of the above statements is true?

Find it here!

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The Only True Statement

How it was tricky & what were others?

One has to be true & other 3 must be false. Let's consider each case one by one.

Case A : According to this statement the number of false statement is 1 which is contrary to given condition that 1 is true & 3 are false. So it can't be true.

Case B : As per this, number of false statements = 2 which is again contrary to given condition of 3 false statements.So it can't be true.

Case C : As per this, number of false statements =3 exactly matching the given condition.

Case D : This implies number of false statements = 4 meaning that all the statements including itself are false. This is opposite to given condition. So this has to be false as well.

So the statement C is true & all other are false!

A Strange Liar

Richard is a strange liar. He lies on six days of the week, but on the seventh day he always tells the truth. He made the following statements on three successive days:

Day 1: "I lie on Monday and Tuesday."

Day 2: "Today, it's Thursday, Saturday, or Sunday."

Day 3: "I lie on Wednesday and Friday."

On which day does Richard tell the truth?

Am I a liar?

Find the truth here!

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Truth Of a Strange Liar

What was his story?

To find the truth we need to logical deduction here.

Now if statement on Day 1 is untrue then Richard must be telling the truth on Monday or Tuesday.

And if Day 3 statement is untrue then he must be telling the truth on Wednesday or Friday.

But he speaks true only on 1 day. So both statements of Day 1 & Day 3 can't be true at the same time. If so, then Richard speaks true on 2 days either Monday/Tuesday or Wednesday/Friday. This means that one of statements from Day 1 must be true & other must be untrue. That also makes the statement on Day 2 untrue always.

Case 1 : Day 3 statement is untrue.

In this case, Richard must be telling truth on either Wednesday or Friday. The statement on Day 1 would be true according to above logical deduction. Hence Day 2 must be either Thursday or Saturday. In both cases, statement on Day 2 would be true.

Case 2 : Day 1 statement is untrue.

If the statement made on Day 1 is untrue then Richard tells truth on Monday or Tuesday. Other statement on Day 3 must be true means Day 3 must be either Monday or Tuesday. If so, then Day 2 must be either Sunday or Monday. In case of Sunday, Day 2 statement would be true & in case of Monday Day 2 statement would be untrue. Hence Day 2 must be Monday & Day 3 must be Tuesday.

So Richard tells truth on Tuesday.

Locker Room & Strange Principal

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has asked the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

Strange task given by principal on first day of school

What principal was trying to teach?

Source

The Lesson Taught By Strange Principal

Where it did begin?

While finding the solution we need to keep basic fact from the problem in mind. Since lockers were closed initially, the lockers which are 'accessed' for odd number of times only are going to open. Rest of all would be closed.

Now task is to find how many such lockers are there which were 'accessed' for odd number of times.

Let's take any number say 24 for example, which is not perfect square & find out how many factors it has.

24 = 1 x 24
24 = 2 x 12
24 = 3 x 8
24 = 4 x 6

So factors are 1,2,3,4,6,8,12,24 i.e. 8 numbers as factors which is even number. Every factor is paired with other 'unique' number! So this pairing always makes number of factors 'even'. In the problem, this lock no.24 will be 'accessed' by 1st, 2nd, 3rd..................24th student. That means 'accessed' even number of time & hence would remain closed.

Now let's take a look at lock no. 16 in which 16 is perfect square. Finding it's factors,

16 = 1 x 16
16 = 2 x 8
16 = 4 x 4

we get 1,2,4,8,16 i.e. 5 numbers as factors which is odd. The reason behind is here 4 appears twice (with itself) while rest of others are paired with other 'unique' number. Hence, number of factors of a perfect square are always odd. Now here lock 16 would be accessed by 1st, 2nd, 4th, 8th, 16th i.e. 5 times. Hence it will be open.

Like this way, every lock with number which is perfect square would be 'accessed' for odd number of times & hence would remain open! e.g. 1,4,9,16,25,49 & so on.

Now 961 (31^2) is the maximum perfect square that can appear within 1000 (32^2) as 1024 goes beyond.

Hence there would be 31 locks open while rest of all closed!

The mathematical fact taught by strange principal

Lesson Of The Day

So what lesson taught by strange principal? The number which is perfect square has odd number of divisors.

Unlock The Distance

Distances from you to certain cities are written below.

BERLIN = 200 miles
PARIS = 300 miles
ROME = 400 miles
AMSTERDAM = 300 miles
CARDIFF = ?? miles

How far should it be to Cardiff ?

Decode The Pattern and Unlock The Distance

How far? Find Here!

Source

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.

The Distance Unlocked after Decoding The Pattern

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

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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?

Connect all the dots with 4 straight lines

Read here how it can be done!

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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!

Connected All The Dots with 4 Straight Lines

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

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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!

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Answer Of Alphamatic Problem

Here is question!

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

ABCABA

BBDCAA

ABEABB

ABDBAA

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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

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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.

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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?

Loss to Shopkeeper Due To Fake Currency Note?

Find that LOSS here!

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'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.

The Shopkeeper lost only Rs.1000 in transaction!

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?

Manufacturers approaches towards some issue!

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!

Simple resolution on complicated concern!

"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.

How to make it shorter without touching it?

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.

How to make line shorter without touching it!

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

To change positions of shorter & longer lines

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

Genius student successfully cracked test by teacher.

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

The problem based on pretty basic formula!

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!

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Neighbor's Solution on Old Farmer's Will