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What others making statements?
Since, each of 4 servants telling different numbers then only 1 of them must be telling the truth & other must be lying.
In that case, all 3 must be having 7 legs i.e. 21 legs while the one who is making true statement must have either 6 or 8 legs. Therefore, there must be 21 + 6 = 27 or 21 + 8 = 29 legs altogether.
Nobody is saying that they altogether have 29 legs but the green octopus is saying that they altogether have 27 legs. Hence, the green octopus must be telling the truth.
A pearl necklace has 33 pearls with the largest and most valuable in the middle.
Starting from one end, each successive pearl is worth $100 more than
the one before (up to the middle one), but starting from the other end
each pearl is worth $150 more than the one before, up to the big pearl.
The whole necklace is worth $65 000.
What is the value of the middle pearl?
Here is the calculation of it's cost!
What is the question?
Let X be the cost of the middle pearl of the necklace.
There are 33 total pearls in the necklace meaning that 16 pearls are on the left and 16 are on the right.
The values of the pearls at the left must be ( X - 100 ), ( X - 200 ),..........( X - 1600 ) and those which are right must have value ( X - 150 ), ( X - 300 ),................( X - 2400 ).
The total value of the pearls at left = ( X - 100 ) + ( X - 200 ) + .......... + ( X - 1600 )
= 16X - 100 ( 1 + 2 + ...... + 16)
The total value of the pearls at left = 16X - 100 (136)
The total value of the pearls at right = ( X - 150 ) + ( X - 300 ) +............... + ( X - 2400 )
= 16X - 150 ( 1 + 2 + ...... + 16)
The total value of the pearls at right = 16X - 150 (136)
Therefore,
The total cost of necklace = The total value of the pearls at left + The cost of middle pearl + The total value of the pearls at right
The total cost of necklace = 16X - 100 (136) + X + 16X - 150 (136)
= 33X - 250 (136)
The total cost of necklace = 33X - 34000
But, the total cost of the necklace given is $65000,
The total cost of necklace = 33X - 34000 = 65000
33X = 99000
X = 3000.
Hence, the cost of the middle pearl is $3000. So the cost of the leftmost pearl is 3000 - 1600 = 1400 and the rightmost pearl is 3000 - 2400 = 600.
If a car had increased its average speed for a 210 mile journey by 5
mph, the journey would have been completed in one hour less. What was
the original speed of the car for the journey?
Here is the calculation of averages speed!
What was the question?
Let S1 be the original speed and S2 be the modified speed and T1 be the time taken with speed S1 and T2 be the time taken with speed S2.
As per given data,
T1 - T2 = 1 hr.
D/S1 - D/S2 = 1 hr.
Here, D = 210 miles, S2 = S1 + 5,
210/S1 - 210/(S1+5) = 1
210(S1+5) - 210s = 1S1(S1+5)
S1^2 + 5S1 - 1050 = 0
(S1-30)(S1+35) = 0
S1 = 30 or S1 = -35.
Since speed can't be negative, S1 = 30 mph.
Hence, the original speed is 30 mph and average speed is 30 + 5 = 35 mph.
With the original speed it would have taken 210/30 = 7 hours but with average speed it took only 210/35 = 6 hours saving 1 hour of time.
99 unique numbers between 1 and 100 are listed one by one, with 5
seconds pause between every two consecutive numbers. If you are not
allowed to take any notes, what is the best way to figure out which is
the missing number?
This is how to correctly guess the missing number!
What was the challenge given?
Just keep up adding the given numbers and remember only the last two digits
of the sum.
The sum of all numbers from 1 to 100 is 5050, so if you
know the sum of all the listed numbers, you will know the missing number
as well.
At the end, if the result is less than 50, subtract it from
50. If the result is larger than 50, subtract it from 150.
Three ants are sitting at the three corners of an equilateral triangle.
Each ant starts randomly picks a direction and starts to move along the
edge of the triangle. What is the probability that none of the ants
collide?
'THIS' is the probability!
What was the problem?
Each ant can decide to go either clockwise or anti-clockwise. That is there are 2 options available for each ant to go. Hence, there will be total 2x2x2 = 8 possible combination of ants' different paths.
Now 2 ants won't collide if & only if all are either moving clockwise or anti-clockwise. In short, out of 8 possible combinations only 2 combinations are there where ants won't collide.
Hence, the probability that ant won't collide is 2/8 = 0.25.
A newspaper made of 16 large sheets of paper folded in half. The
newspaper has 64 pages altogether. The first sheet contains pages 1, 2,
63, 64.
If we pick up a sheet containing page number 45 what are the other pages that this sheet contains?
Here is the solution of puzzle!
What was the puzzle?
If the page starts with odd number 1 & back side followed by even 2 then at the back of page number 45, there must be number 46.
Generally, for the page p, page 65 - p shares the same sheet as p. Like page 1 and 65-1 =64, page 2 and 65-2=63 page are on the same sheet.
Therefore, page 45 must be on the same sheet as 65 - 45 = 20 page number. And the page 46 must be on the same sheet as page 65 - 46 = 19.
In short, the pages 19,20,45 and 46 must be on the same sheet.
Sara needs to trek from an oasis to a destination 10 miles away across a barren desert.
The facts:
- Crossing one mile of desert requires using 1 gallon of water.
- Sara can only carry 6 gallons of water at a time.
- Sara can drop a water cache (of any amount of water from the supply
she is carrying at that moment) at any of the nine stops along the
route, and then pick up any part of the cache on a later trip.
What's the minimum number of times Sara must leave the oasis in order to cross the entire 10 mile span of desert?
This is how she optimizes her journey!
What was the challenge in journey?
1. First Sara collects 12 gallons of water at milepost 1 after having 3 trips from source. She uses 2 gallons (out of 6) for forward & backward journey from source to milepost & dropping 4 gallons in cache at milepost 1.
2.She collect 6 gallons more water at the start of 4th trip from source & drops 5 gallons at milepost 1. Now, she doesn't need to return back to source and 17 gallons of water available at milepost 1.
3.In next 2 rounds, she moves 8 gallons of water from milepost 1 to milepost 2 (1 for forward + 4 for drop + 1 for backward journey in each round).
4.Now only 5 gallons left at milepost 2. She uses 1 gallon for journey from milepost 1 to milepost 2 and drop remaining 4 gallons at milepost 2. Now, 12 gallons of water is available at milepost 2.
3.Next, using 2 gallons (out of 6 which is maximum she can carry) she moves from milepost 2 to milepost 4 and drop 2 gallons at milepost 4 & comes back at milepost 2 using remaining 2.
4. Again, on arriving back at milepost 2, she has left with 6 gallons of water at milepost 2 out of which she uses 2 to reach milepost 4 where 2 gallons of water still available there already collected in previous round. Now, she doesn't need to return back from
milepost 4.
5. She uses the remaining 6 gallons of water to reach at the milepost 10.
To conclude, Sara has to leave Oasis only 4 times as describe in steps 1 and 2 if she want to cross the entire 10 mile span of desert.
A dead body lies at the bottom of a multistory building. It looks as though he committed suicide by jumping from one of the floors.
When the detective arrives, he goes to the first floor of the building, opens the closed window, and flips a coin towards the floor. He goes to the second floor and does the exact same thing. He continues to do this until he gets to the top floor of the building.
When he comes back down, he states that it was a murder and not a suicide. How does he know that?
(Entry to the terrace was banned due to some ongoing work).
Read the detective's logic in the case!
What is the case?
Obviously, the person can't jump with window closed or come outside of the window & close that window from inside.
The detective checks if windows is closed from inside by opening window & flipping the coin toward the floor. He flips the coin to mark the count of that particular floor where window was closed from inside & he has to open it to flip the coin.
At the end, he collects as many coin as floors of that building. So he concludes that no floor had open window from where the person might have jumped.
So, he concludes that it was the murder and not the suicide.
Four glasses are placed on the corners of a square table. Some of the
glasses are upright (up) and some upside-down (down). A blindfolded
person is seated next to the table and is required to re-arrange the
glasses so that they are all up or all down, either arrangement being
acceptable, which will be signaled by the ringing of a bell.
The
glasses may be re-arranged in turns subject to the following rules.
1.Any
two glasses may be inspected in one turn and after feeling their
orientation the person may reverse the orientation of either, neither or
both glasses.
2.After each turn the table is rotated through a random
angle.
3.The puzzle is to devise an algorithm which allows the blindfolded
person to ensure that all glasses have the same orientation (either up
or down) in a finite number of turns. The algorithm must be
non-stochastic i.e. it must not depend on luck.
Here is that algorithm!
What was the puzzle?
Below is the algorithm which makes sure the bell will ring in at most five turns.
1.On the first turn choose a diagonally opposite pair of glasses and turn both glasses up.
At this point, the position of other 2 glasses is not known.
2.On the second turn, choose 2 adjacent glasses. One of them was turned up in the previous step, so other may or may not in up position. If the other is down then turn it up and if remaining one X is also in up position then bell will be rung.
If the bell does not ring then there are now three glasses up and one down(3U and 1D).
3.On the third turn choose a diagonally opposite pair of glasses. If one is down, turn it up and the bell will ring.
And if you find both are up, then you must have chosen other diagonally opposite pair.
If so, then turn one down so that 2 glasses are up and other 2 are down.
4.On the fourth turn choose two adjacent glasses and reverse both. If both were in the same orientation then the bell will ring.
And in case, if you find one is up and other down like -
still reverse orientation of both as -
Now diagonally opposite pairs are either up or down.
5.On the fifth turn choose a diagonally opposite pair of glasses and reverse both.
The bell will ring for sure.
A solid, four-inch cube of wood is coated with blue paint on all six
sides.
Then the cube is cut into smaller one-inch cubes. These new
one-inch cubes will have either three blue sides, two blue sides, one
blue side, or no blue sides. How many of each will there be?
Here is solution of the puzzle!
What is the puzzle?
Apart from the 8 cubes at the center all 4 x 4 x 4 - 8 = 56 will have some paint on ones side at least. See below the 1/4 th cube is taken out.
The cubes at the 8 corners will have blue paint on three sides.
The cubes between corner cubes along 12 edges of big cube will have 2 sides painted. That is 12 x 2 = 24 cubes will painted with blue on 2 sides.
And 4 center cubes on each of 6 faces (left, right, top, bottom, front, back) will have only 1 side painted with blue. That is , there are 6 x 4 = 24 cubes having paint on one side only.
To conclude, out of 56 painted cubes,
24 cubes have paint on 1 side,
24 cubes painted with 2 sides,
8 are painted with three sides.
This puzzle has been attributed both to Lewis Carroll and to Albert Einstein:
- There are five houses in a row. Each of the houses is painted a
different color, and their occupants come from different countries, own
different pets, drink different beverages, and smoke different cigarette
brands.
- The Englishman lives in the red house.
- The Spaniard owns the dog.
- Coffee is drunk in the green house.
- The Ukrainian drinks tea.
- The green house is immediately to the right (your right) of the ivory house.
- The Old Gold smoker owns snails.
- Kools are smoked in the yellow house.
- Milk is drunk in the middle house.
- The Norwegian lives in the first house.
- The man who smokes Chesterfields lives in the house next to the man with the fox.
- Kools are smoked in the house next to the house where the horse is kept.
- The Lucky Strike smoker drinks orange juice.
- The Japanese smokes Parliaments.
- The Norwegian lives next to the blue house.
Who drinks water? Who owns the zebra?
Well, here is effort to simplify the solution
From Wikipedia : The puzzle is often called Einstein's Puzzle or Einstein's Riddle because it is said to have been invented by Albert Einstein as a boy; it is also sometimes attributed to Lewis Carroll. However, there is no known evidence for Einstein's or Carroll's authorship and the Life International version of the puzzle mentions brands of cigarette, such as Kools, that did not exist during Carroll's lifetime or Einstein's boyhood.
