### #1 - IAS Logic Problem

Anabelle is a clever trader of rare artifacts. Each day she carries three boxes with each filled with thirty artifacts. The boxes cant 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 ?

Anabelle is no dumb trader and she knows the strategy with the help of which she will be able to save 25 artifacts even after passing 30 check points.

All she will focus on is getting rid of the boxes as soon as possible.

To shed the first sack quickest possible, she will start filling artifacts from one box to other two. Assume that she is able to do that after passing through A check points.

(Space in first box) A + (Space in second box) A = (Remaining artifacts in third box) 30 -A
A = 10

Therefore, after 10 check points, she will be left with two boxes with 30 artifacts each. Now to get rid of the second box, she will start filling artifacts from second box to first box. Let us assume that she is able to get rid of the second box after B checkpoints.

(Space in first box) B = (Remaining artifacts in second box) 30 - B
B = 15

Therefore, after fifteen check points, she will be left with one sack with thirty artifacts in it.

Since she has five more check points left, she will have to give five more artifacts and after passing them all, she will still have 25 artifacts.

### #2 - Mind Boggling Puzzle

It's time for a mind boggling puzzle.Analyze the statements below and find out who did it.

Please note that three of the statements below are false.

1. Mr. Reese: 'Mr. Bilbo did it.'
2. Mr. Bilbo: 'Mr. Reese did it.'
3. Mr. Gerry: 'Mr. Bilbo’s telling the truth.'
4. Mr. Yang: 'Mr. Gerry’s not lying.'

Mr. Bilbo did it.

Let us consider all the statements one by one for every person and find out.

Case 1: Mr. Bilbo did it, then
Statement 1 => true
Statement 2 => false (as Reese did not do it)
Statement 3 => false (as Mr. Bilbo is lying)
Statement 4 => false (as Mr. Gerry is lying)
It was Mr. Bilbo who did it. But let us confirm by taking up other cases as well.

Case 2: Mr. Reese did it, then
Statement 1 => false (as Mr. Bilbo did not do it)
Statement 2 => true
Statement 3 => true (as Mr. Bilbo is not lying)
Two statements are true whereas only one should be true, thus Mr. Reese did not do it.

Case 3: Mr. Gerry did it, then
Statement 1 => false (as Mr. Bilbo did not do it)
Statement 2 => false (as Mr. Reese did not do it)
Statement 3 => false (as Mr. Bilbo is lying)
Statement 4 => false (as Mr. Gerry is lying)
All four statements stand false, thus Mr. Gerry did not do it.

Case 4: Mr. Yang did it, then
Statement 1 => false (as Mr. Bilbo did not do it)
Statement 2 => false (as Mr. Reese did not do it)
Statement 3 => false (as Mr. Bilbo is lying)
Statement 4 => false (as Mr. Gerry is lying)

All four statements are false therefore Mr. Yang did not do it.

We have verified with everyone and now know that it was Mr. Bilbo who did it.

### #3 - Deductive Reasoning Logical Problem

There are 4 big houses in my home town.

They are made from these materials: red marbles, green marbles, white marbles and blue marbles.

* Mrs Jennifer's house is somewhere to the left of the green marbles one and the third one along is white marbles.
* Mrs Sharon owns a red marbles house and Mr Cruz does not live at either end, but lives somewhere to the right of the blue marbles house.
* Mr Danny lives in the fourth house, while the first house is not made from red marbles.

Who lives where, and what is their house made from ?

From, left to right:
#1 Mrs Jennifer - blue marbles
#2 Mrs Sharon - red marbles
#3 Mr Cruz - white marbles
#4 Mr Danny - green marbles

If we separate and label the clues, and label the houses #1, #2, #3, #4 from left to right we can see that:
a. Mrs Jennifer's house is somewhere to the left of the green marbles one.
b. The third one along is white marbles.
c. Mrs Sharon owns a red marbles house
d. Mr Cruz does not live at either end.
e. Mr Cruz lives somewhere to the right of the blue marbles house.
f. Mr Danny lives in the fourth house
g. The first house is not made from red marbles.

By (g) #1 isn't made from red marbles, and by (b) nor is #3. By (f) Mr Danny lives in #4 therefore by (c) #2 must be red marbles, and Mrs Sharon lives there.

Therefore by (d) Mr Cruz must live in #3, which, by (b) is the white marbles house.

By (a) #4 must be green marbles (otherwise Mrs Jennifer couldn't be to its left) and by (f) Mr Danny lives there.

Which leaves Mrs Jennifer, living in #1, the blue marbles house. QED.

### #4 - Explain Murder Mystery Riddle

You are living at you place alone. You own a shed which has been locked. The lock that has been placed on the door can be closed without a key but need the key to be opened. You collected some old stuff and decided to keep it in the shed. After keeping the things, you locked it back. The next day, the police found a dead body inside the shed. As you are the only one living in your house, the police has nothing else to believe than you are the murderer. But you have not committed any crime.

There is a way the murder would have happened. Can you find that way and tell the police so you are not sentenced for the crime you did not commit?

The lock can be closed without a key.
When you were keeping the things inside the shed, the murderer took the lock hanging on the door and replaced it with an identical one. You closed it as it did not require a key. When you were gone, the murderer opened the new lock with his key, planted the body inside, replaced the lock with the original one again and locked it.

### #5 - Card Puzzle

In two decks of cards, what is the least amount of cards you must take to be *guaranteed* at least one four-of-a-kind?

Forty.

The number of decks is irrelevant; the answer is the same if one or one-hundred decks are used.

Any card drawn will be a A,2,3,4,5,6,7,8,9,10,J,Q, or K, so there are 13 possibilities each time a card is drawn.

The fastest way to draw a four of a kind is if the first four cards all have the same 'value.' The slowest way, which provides the solution, is to first draw 13 three of a kinds, and then one more card.

Since 13 x 3 + 1 = 40, if 40 cards are drawn it is guaranteed that those forty cards contain at least one four of a kind.

### #6 - Logical Puzzle

There are five men, let's say Tarun Harish Lavesh, Manoj, and Manish. All of them have a dot mark in their forehead. They can't see the dot on their own forehead, but can see the ones on others. The owner of WHITE dot is an honest person and will never lie, while the owner of BLACK dot always tell the lie.

This is the statement from Tarun Harish Lavesh, and Manish:
Tarun: 'I see 3 whites and 1 black'
Harish: 'I see 4 black'
Lavesh: 'I see 3 black and 1 white'
Manish: 'I see 4 white'

What color is the dot on each Tarun Harish Lavesh, Manoj, Manish forehead?

Tarun Harish Lavesh, and Mansih stated a contradiction statement, so only one of them can said the truth.
We don't know yet where Manoj stands, it's still possible that he has black or white color.
Thus, the maximum possibility of white dots are 2, that is Manoj and 1 of Tarun Harish Lavesh, and Manish.
Tarun and Manish obviously told the lie, as they said there are 3 and 4 person has white dot, which leave us Harish and Lavesh .
Assuming Harish is white, then he must be telling the truth that he saw 4 black dots, which makes Lavesh a liar. This is an impossible situation, since Lavesh saw 3 black and 1 white (Lavesh has to be a liar, so there must be more than 1 white, meaning it's impossible Harish saw 4 blacks).
The only possibility is Lavesh told the truth.
So, Tarun Harish Manish have black dots, while Lavesh and Manoj have white dots.

### #7 - Dating Puzzle

katrina wants to go on a date and prefers her date to be tall, dark and handsome.

Of the preferred traits - tall, dark and handsome - no two of Shahrukh, Ajay, Salman and Akshay have the same number.
Only Shahrukh or Akshay is tall and fair.
Only Ajay or Salman is short and handsome.
Shahrukh and Salman are either both tall or both short.
Ajay and Akshay are either both dark or both fair.
Who is katrina's date?

Salman is katrina's date.

As no two of them have the same number of preferred traits - from (1), exactly one of them has none of the preferred traits and exactly one of them has all the preferred traits.

From (4) and (5), there are only two possibilities:
* Shahrukh & Salman both are tall and Ajay & Akshay both are fair.
* Shahrukh & Salman both are short and Ajay & Akshay both are dark.

But from (2), second possibility is impossible. So the first one is the correct possibility i.e. Shahrukh & Salman both are tall and Ajay & Akshay both are fair.

Then from (3), Ajay is short and handsome.

Also, from (1) and (2), Shahrukh is tall and fair. Also, Akshay is the person without any preferred traits. Salman is Dark. Shahrukh and Salman are handsome. Thus, following are the individual preferred traits:

Salman - Tall, Dark and Handsome
Shahrukh - Tall and Handsome
Ajay - Handsome
Akshay - None :-(

Hence, Salman is katrina's date.

### #8 - Deductive Reasoning Puzzle

Six lovely girls are standing in a straight line such that
1. X and W are neighbors of Y.
2. V's only neighbor is U.
3. U is at the forth place of Z.

So who two are standing at the 2 corner of the line ?

V and Z

Solution: According to given information, sitting arrangement of six people is -

V U X Y W F or Z X Y W U V or V U W Y X Z or Z W Y X U V

So, in all the situations, Z and V are at corners of the row.

### #9 - Logic Detective Problem

A hen, a dog, and a cat are stolen. Three suspects are arrested named Robin, Steve, and Tim. The police are sure that all of them stole one of the animals but they don't know who stole which animal.

Sherlock Holmes is appointed to identify and is provided with the following statements from the investigation.

Robin - Tim stole the hen
Steve - Tim stole the dog
Tim - Both Robin and Steve are lying. I neither stole hen, nor dog.

Sherlock is somehow able to deduce that the man who stole the cat is telling a lie and the man who stole the hen is telling truth.

Can you help him find out who stole which animal?

Robin Stole Cat
Steve stole Hen
Tim Stole Dog

Glance at the first and second statement again; they are contradictory. Both can be true together though. Also both of them cannot be false which means that Tim stole cat and his statement will be true. But it has been already deduced that the one who stole cat was telling a lie thus it can’t be possible.

Let us consider the situation again. It may be that Tim stole a hen or a dog. Assume that he stole hen. In such a case the statement of Tim will be false. But we know that the person who stole hen told the truth, thus it is contradicting our assumption and so cannot be correct.

Considering everything, now we can say with confidence that Tim stole the dog.

Now it means that the statement by Robin is completely false and the statement by Steve is true which depicts that the cat and hen are stolen by these two. Also we know that the one who stole hen is true and the one stealing cat is a liar. Thus we now know that Robin stole cat and Steve stole hen.

### #10 - Logical Valentine Day Lucky Problem

Katrina, kareena, Priyanka and Deepika visited me on the valentine's Eve.

The time of each visit is mentioned below:
A) Katrina at 8:00
B) kareena at 9:00
C) Priyanka at 10:00
D) Deepika at 11:00
*Each time mentioned above may be either AM or PM.

Also below statements hold true:
A) Priyanka did not visit me between kareena and Deepika.
B) At least one female visited me between Katrina and kareena.
C) Katrina did not visit me before both Priyanka and Deepika.

Can you tell at what time did they individually visit me ?

kareena (9:00AM) - Deepika (11:00AM) - Katrina (8:00PM) - Priyanka (10:00PM)

From the given data, it is clear that at least one female visited me in the morning and at least one female visited me in the evening. Also, from (4), Katrina did not visit me first. It means that Katrina visited me at 8:00 PM. From (3), kareena must have visited me at 9:00 AM. Also, either Priyanka or Deepika or both visited me in the morning. But from (2), only Deepika must have visited me in the morning at 11:00 AM and hence, Priyanka visited me at 10:00 PM.