#501 - Thoughtworks Interview Logic Puzzle

There are ten boxes containing some balls. Each of the ball weighs exactly 10 grams. One of those boxes have defective balls (all the defective balls weigh 9 grams each).

An electronic weighing machine is provided to you and you are allowed only one chance of weighing on it.

How will you find out which box has defective balls ?

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Let us simplify boxes by naming them from 1 to 10.
Now the trick here is to pick different number of balls from different boxes. So to simplify things, we will pick balls corresponding to box number.

Thus, pick 1 ball from Box 1, 2 balls from box 2, 3 balls from box 3 and so on. You will have 55 balls altogether. Now, put them all in the balance.

If all balls were weighing accurate 10 grams, the total weight of the 55 balls would have been 550 grams. But one of the box must have had the defective balls.

Suppose if the defective balls were in box number 2, then the total weight will be 2 grams less than 550. If the defective balls were in box 8, the total weight will be less than 8 grams from 550. In this way, you will be able to identify which box has the defective balls.

#502 - Two Rectangles Two Matchsticks Puzzle

Can you move two matchsticks in the given picture in a manner that the resulting arrangement comes up with two rectangles?

Two Rectangles Two Matchsticks Puzzle
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See the image to find out how we did it. PS: Square is also a rectangle.

#503 - Missing Number Row Sequence

Can you find the missing number in the third row?
35 20 14
27 12 18
5 2 ?

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The missing number is 20.

Here (left number / middle number) * 8 = right number
E.g. (35 / 20) * 8 = (7/4) * 8 = 7 x 2 = 14
You can follow the same to find out the remaining digit.

#504 - Confusing Probability Puzzle

You along with your friend are standing in front of two houses. Each of those houses inhabits a family with two children.

Your friend tells you the below two facts:
1) On your left is a family that has a boy who likes accounts but the other child loves science.
2) On the right is a family with a seven year old boy and a new born baby.

You ask him, "Does either of the family have a girl?"

To this he replies, "I am not quite sure. But can you guess that? If you are right, I will give you $200."

Which family do you think is likely to have a girl ?

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1/2

In the house on the left, there are three possibilities:
Younger Older
Girl Boy
Boy Girl
Boy Boy

We cant have a girl-girl option because it has been mentioned that there is at least one boy in that house. Now all these outcomes are equally likely, and we have two events with girls, the chances of having a girl in the left house is 2/3.

In the house on the right, there are two possibilities because we already know that the older child is a boy:
Younger Older
Girl Boy
Boy Boy
Here the chances are 1/2.

Thus you must choose the house on the left for better chances at winning.

#505 - Knights Tour Chess Puzzle

In the picture, you can see a chess board. On the top left position, the K marks a knight. Now, can you move the knight in a manner that after 63 moves, the knight has been placed at all the squares exactly once excluding the starting square?

Knights Tour Chess Puzzle
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As you can see in the picture, the strategy used here is to cover the border first and then move to the inner squares.

#506 - Four Squares Matchsticks Puzzle

In the formation, you can see a few arranged matchsticks. Can you form three squares by moving just three matchsticks ?

Four Squares Matchsticks Puzzle
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The figures shows how to do it.

#507 - Who Is The Murderer Riddle

Role Action
Block Prevents the target player from acting
Redirect Change target player target.
Save Protects the target player from death.
Seer Sees all actions that occurred
Murderer Kills the target player

Following five players are playing:
Andy
Brian
Chris
Daniel
Fred

You are Andy the Seer and you saw the following things:
a) Brian was redirected to Chris.
b) Chris was blocked.
c) Daniel was killed.

Who is the murderer then?

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The murderer is Fred.

Andy is the seer so exclude him.
Now, if Brian was murderer, then Chris should have been killed.
Now we know that Chris was blocked. Therefore he cannot be the murderer.
Daniel cant be the killer as he was killed himself.
This leaves with Fred.

#508 - Trick Story Puzzle

A man was telling some of his war stories to his grandchildren.
"When the World War I was on the verge of end, I was awarded for my bravery for I had saved a group of my men." He coughed and then added, "When we were fighting in northern France, an enemy soldier threw a grenade at us. Before it could explode, I picked it up and threw it away. For my act of bravery, right before the war ended, A General gave me a sword engraved with the words "Awarded for Display of Bravery and Heroism in World War 1"."

Hearing this, one of the grandson spoke up. "Grandpa, this is not a true story. It can"t be true!"

The truth is that it was not. How did the grand children know it?

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The word "World War I" could not have been engraved on the sword. This is because the Second World War had not happened then and nobody knew that it will happen.

#509 - Famous Chess Board Puzzle

In a chess board, the queen piece can movie horizontally, vertically and diagonally freely. The picture represents the same.Can you place 8 queens on the board in a manner that none of the queens can attack each other?

Famous Chess Board Puzzle
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See the image to find out how it can be done.

#510 - Hard Tricky Maths Trivia Question

Can you think of three numbers that gives a prime number as their product and also the difference between the second and first is equal to the difference between third and second?

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The three numbers are: -3, -1 and 1.
Remember that we never asked for positive numbers.