Cakes For Grandma's Birthday

What's between you & grandma's birthday celebration? 

No need to overthink on this. Just carry 2 cakes.

At each toll they would take 1 ( half of 2 ) & would give back 1.

So after each toll you would carry 2 cakes & last toll wouldn't be an exception.

Squares From Squares Challenge

In the picture that is attached with this question, you can find a square which comprises of four little squares inside it. Consider this square to be made with matchsticks. You have to remove two matchsticks such that only two squares remain instead of five.How will you do it ?

Make it 2!

Challenge accepted here! 

Source 

Squares From Squares Challenge Accepted

What was the challenge? 

All that you need to do is that remove these 2 match sticks labelled in figure below.

So we get exactly 2 squares as below.

What is Sister-7 doing ?

There are seven sister in a house in a village where there is no electricity or 

any gadget.

Sister-1: Reading Novel

Sister-2: Cooking

Sister-3: Playing Chess

Sister-4: Playing Sudoku

Sister-5: Washing clothes

Sister-6: Gardening


what is Sister-7 doing ? 

She must be..... 

Source 
 

Playing The Chess Alone?

First read the question. 

Sister -7 must be playing Chess with Sister-3.Remember there is no gadget in room.So sister -3 must not be playing Chess on a smartphone, tablet, laptop or desktop PC (no electricity). Every other activity can be done individually but for playing Chess you need partner at the other end.

A Clever Trader At Checkpoints

Anabelle is a clever trader of rare artifacts. Each day she carries three boxes with each filled with thirty artifacts. The boxes can't hold more than that. She travels far of northern lands to sell these artifacts but on way, she comes across thirty checkpoints where she has to shed one of the artifact for each sack to the authorities for letting her pass.

How many artifacts will be left with her when she reaches her destination crossing all the check points ?  

How she managed to save some? Find here! 

Source
 

A Cleaver Trader's Deal At Checkpoints

What was the situation?

Without any work to brain if she travels as it is through all checkpoints then at the end nothing would be left with her. Because at each checkpoint she has to shed 3 artifacts so at 30 checkpoints she has to shed 3 x 30 = 90 artifacts if she gives artifact from each box. And she has only 90 artifacts.

As a clever trader, she starts shedding artifacts from one box at each checkpoint. At first 10 checkpoints, 1 box would be emptied & 30 artifacts paid at checkpoints.

For next 15 checkpoints, she sheds all artifacts from second box thereby paying 30 artifacts.

For final 5 checkpoints, now she has to shed only 5 artifacts from third box with 25 artifacts remaining in the box.

So 25 artifacts will be left with her when she reaches her destination crossing all the check points.

Initial Amount in Wallet?

On the festival of Raksha Bandhan (holy festival where brother-sister relationship celebrated), Mayank decides to visit his 3 sisters. He takes certain amount with in his wallet & goes to first sister. While without his notice first sister puts equal amount of money as in wallet. After tying rakhi, Mayank gifts her Rs.2000. Now he moves to second sister. While Mayank takes a breakfast, the second sister secretely doubles the money that was in Mayank's wallet. Again after tying rakhi, Mayank gifts her Rs.2000. At third sister's home, while he enjoys delicious lunch cooked by his sister, third sister doubles money in his pocket. Once again after tying rakhi, Mayank gifts third sister Rs.2000.Now there were Rs.5000 in his wallet.

How much amount Mayank had taken while leaving his home?

How much amount? Find it here! 

Simple Calculation for Initial Amount

What was the puzzle? 

We need to go backward to get the answer.

3. At third sister's home he had 2000 + 5000 = 7000. So before visit he had 7000 / 2 = 3500.

2. At second sister's home he had 3500 + 2000 = 5500. This 5500 were doubled from his existing 2750 by her second sister.

1. At first sister's home he had 2750 + 2000 = 4750. His first sister had added 4750 / 2 = 2375 to his wallet in which there were Rs. 2375 already.

So Mayank took Rs. 2375 with him in his wallet while he left home.

However, Mayank must had idea of that his sisters added money to his wallet without his attention.

 

Abnormal Looking Normal Puzzle

A donkey travels the exact same distance daily. Strangely 2 of his legs

travels 40 kilometers and the remaining two travels 41 kilometers. 

Obviously 2 donkey legs cannot be a 1km ahead of the other 2.

The donkey is perfectly normal. So how come this be true ?

 I'm perfectly normal!

Why so? Find it here! 

Source 

That Looks Perfectly Normal

What was looking abnormal? 

The donkey is moving on a circular path. Hence, his 2 legs on right (or left depending on moving clockwise or anticlockwise) moves along a circle having lesser radius than circle on which left legs are moving. The difference in circumferences of circles accounts the difference in distance traveled.

Winner Deserving The Scholarship

This is my favorite puzzle which I had read in a newspaper. It really makes you to think more & more logically to get the answer. I had posted it back in July but re posting it here.

"The scholarship will be awarded," said the head to three candidates - Chuckles, Wombat & Breeze - "to the winner in this little competition. I am going to chalk a cross, which will be either a green or a red cross. I shall then ask each one who can see a green cross to hold his hand up; and take his hand down as soon as he can tell me what his own cross is. He must, of course, be able to explain how his answer is arrived at. Kindly close your eyes for 10 seconds."

He chalked a green cross on all three foreheads. "Go!"

All three hands shot up in air ; that of Chuckles was almost immediately lowered. "My cross is green , Sir"

How did Chuckle know?
  
Read here how the story unfolds!



 

Popular Missing Square Puzzle

How many number of times you have come across this image?

By now, you might have accepted the solution.

"The hypotenuse is bulged in bottom figure which accounts area equal to missing square!"

But is this really a solution to this puzzle? The issue illustrated in clear manner here!

And my opinion is here!

And how creator did manage to create that 'missing' square is illustrated here!

 

Jumping Safely From 33rd Floor?

A man was gazing through the window of the 33rd floor of the building. He suddenly opened the window and jumped on the other side of the window. On landing the floor, there was not a sheer mark of injury on him.

How can that be possible if he did not use any kind of parachute and did not land on a soft surface ? 

  
Why he landed safely? Find Here! 

Jump Causing No Injury

But why to jump? 

The man was cleaning the window of 33rd floor & jumped inside the room through the window after finishing his work. Jumping from few feet from landing floor rarely causes any injury.

Crossing The River In Minimum Time

Four people need to cross a dark river at night. They have only one torch and the river is too risky to cross without the torch. If all people cross simultaneously then torch light won't be sufficient. Speed of each person of crossing the river is different. Cross time for each person is 1 min, 2 mins, 7 mins and 10 mins. 

However 2 can cross together but there is one limitation.If two are crossing the river then it takes time equal to slowest person would take alone. For example, if persons with cross times 1 min & 10 mins are crossing then it would take 10 mins for both to cross the river.

What is the shortest time needed for all four of them to cross the river ? 

  
Find here the efficient way! 

Source 

Efficient Way To Cross The River

What's the challenge? 

Let's name each person by their crossing times as 1,2,7,10.

The instant solution that everyone can think of is using 1 as a usher to guide all. That means 10 & 1 goes, 1 comes back; 7 & 1 goes again 1 comes back and 2& 1 goes finally. This would take 10 + 1 + 7 + 1 + 2 = 21 mins to cross rivers.

Is it really efficient solution? What if we find a way to cross both 10 & 7 in one go & other 1 waiting across to bring back torch.

1. The 1 & 2 goes across but 1 comes back - 2 + 1 = 3 mins required.

2. Now 10 & 7 goes across & send 2 back with torch - 10 + 2 = 12 mins required.

3. Finally after coming back 2 & take 1 across the river - 2 minutes required.

So total 3 + 12 + 2 = 17 minutes required to cross the river for those 4 persons. In first step, 2 can also come back & send 10 & 7. In that case, in second step, 1 has to come back to take 2 across the river. Isn't this a more practical solution? 

Hijacker's Strange Demand!

A man hijacks an aeroplane transporting both passengers (8 of them) and valuable cargo.After taking the cargo, the man demands nine parachutes, puts one of them on, and jumps, leaving the other eight behind. Why did he want other eight?

          I want 9!

Find the reason here! 

Source 

Hijacker's Safe Game!

And how did he play it? 

Had he demanded single parachute how can he be sure that it's not adefective one. He demanded nine with thought that cops would think that he wants to jump with all 9 passengers safely. So cops would not take risk of sending any defective parachute. 

Fill in the blanks

Place the numbers 1 through 9 in the circles below, such that each side of the triangle adds up to 17.

Fill Numbers

Find those circles filled here! 

Correct Numbers in Blanks

What was the challenge? 

Just putting at 1,2 & 3 at 3 corners of triangle leaves only thing to find other 2 numbers giving total sum 17. Have a look at below.

   Correct Numbers in Blanks

 

Birbal The Wise!

Emperor Akbar once ruled over India. He was a wise and intelligent ruler, and he had in his court the Nine Gems, his nine advisors, who were each known for a particular skill. One of these Gems was Birbal, known for his wit and wisdom. 

The story below is one of the examples of his wit. Do you have it for you to find out the answer? 

A farmer and his neighbor once went to Emperor Akbar"s court with a complaint. "Your Majesty, I bought a well from him," said the farmer pointing to his neighbor, "and now he wants me to pay for the water." "That"s right, your Majesty," said the neighbor. "I sold him the well but not the water!" The Emperor asked Birbal to settle the dispute. 

Now it's very difficult to think what Birbal had in his mind at that time. Still you can give a try. How did Birbal solve the dispute? 

Read here how Birbal rescued the farmer! 

Source 

Justice WIth The Farmer

What's the story behind the title? 

"So you have sold the well to the farmer but not the water?" Birbal asked the neighbor. 

"Do you agree that owner of well is the farmer & you are owner of water?" Birbal asks further.

"Exactly!", neighbor replied.

Birbal now points towards the valid question - "So you need to pay rent for keeping your water in his well, or take out all of the water out of well. Don't you?"

By now the neighbor realized that he was outwitted. He had no option other than to apologize & take back his claim.

Who knocked over the monitor?

Melissa and Jessica were working on the computer along with their friends Sandy and Nicole.  Suddenly, I heard a crash and then lots of shouts.  I rushed in to find out what was going on, finding the computer monitor on the ground, surrounded with broken glass!  Sandy and Jessica spoke almost at the same time:

Jessica saying, "It wasn't me!"

Sandy saying, "It was Nicole!"

Melissa yelled, "No, it was Sandy!"

With a pretty straight face Nicole said, "Sandy is a liar."

Only one of them was telling the truth, so who knocked over the monitor? 

Find here who did it! 

Source 
  

Person Who knocked Over Monitor!

What's the entire matter? 

If we assume Jessica speaking the truth & she is not the culprit then other 3 must be liar. The truth that comes from Nicole's statement is that Sandy is telling truth. But only 1 is speaking truth not 2 as here Sandy & Jessica.

That means Jessica is lying. Which in turn means it was she who done that damage. Now Sandy's statement can't be true as we already have got culprit Jessica. 

Similarly, Mellisa lying as she is pointing towards Sandy.Two person not telling truth at a time as per provided information.

So only left with Nicole who is telling the truth that Sandy is liar.

Hence we can conclude that, Jessica knocked over the monitor & Nicole is telling the truth.

Who is Liar?

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?)

This should be that question! 

Source 

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.

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! 

 Source

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! 

Source 

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?

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!

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 ?

 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. 

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)

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

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