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?
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, "Sandyis a liar."
Only one of them was telling the truth, so who knocked over the monitor?
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.
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?)
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.
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 onMondayor Tuesday.
And if Day 3 statement is untrue then he must be telling the truth onWednesdayorFriday.
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 eitherWednesday orFriday. 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.
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 eitherMondayor Tuesday. If so, then Day 2 must be either
Sunday or Monday. In case ofSunday,Day 2 statement would be true & in case of Monday Day 2 statement would be untrue. Hence Day 2 must beMonday& Day 3 must be Tuesday.
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?
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.
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.
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
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".
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)
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-
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!
In the addition below, all digits have been replaced by
letters. Equal letters represent equal digits and different letters
represent different digits.
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.
First of all let's write down the equation once again.
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.
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.
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.
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.
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.200to 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.
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?
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!
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 linelooked longer & right one shorter!
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
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
After 1 hour, all 3 bodies stop moving. What is the total distance traveled by the bug?
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
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
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.
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
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!
A man in depression decided to commit suicide. He started walking along a railway track when he spotted an express train
speeding towards him. Suddenly he changes his mind & decides not to suicide. To avoid it, he jumped off the track, but before
he jumped he ran ten feet towards the train.
Since the man was firm on his decision of ending his life he started to walk on a railway bridge. By doing that, he made sure no body would save him & even if he falls in river, the death is sure as he didn't know swimming. After crossing the bridge more than half way, he changed his mind. Now by running back wouldn't be feasible option as train was speeding towards him at greater speed. Only way to save life was cross the bridge before train hits him.
Hence he ran 10 feet towards the train & jumped off the track thereby to save his life.
You have 10 bags of gold coins.You have appointed 1 servant to carry each bag. One of your servants who
were responsible for transport of the money wanted to trick you. He
took one of the bags and filed away one gram of gold from each
coin. One coin normally weighs 10 grams.
you figure out in one scaling which bag contains lighter coins? Which
servant should be fired? – using digital scales (shows the exact weight
of an item)?
We need to take coins from each of 10 bags to test.
Number all the servants & their respective bags from 1-10. Now take 1 coin from first bag, 2 coins from second bag, 3 coins from third bag & so on to 10 coins from tenth bag. Put all those on digital scale. In normal case, with no corruption it would weighin the caseas 55 x 10 = 550 gm. But coins from one of the bag weighs 1 gm less. So if it weighs 1 gm less then 1st coin that came from first bag is filed one & hence first servant is corrupt. If it weighs 548 gm then coins from second bag are reduced ones & hence second servant is corrupt.
Depending on how many gm less than 550 gm it weighs the bag with manipulated coins can be identified & respective servant can be fired.
A man is the owner of a winery who recently passed away. In his will, he left 21 barrels (seven of which are filled with wine, seven of which are half full, and seven of which are empty) to his three sons. However, the wine and barrels must be split, so that each son has the same number of full barrels, the same number of half-full barrels, and the same number of empty barrels.
Note that there are no measuring devices handy. How can the barrels and wine be evenly divided?