Who Lives Where?

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 ?

HERE is step by step process to know who lives where! 

Location and Owner of Each House

What are the hints given?

Take a look at the given details once again - 

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

1. Mrs Jennifer's house is somewhere to the left of the green marbles one.

2. The third house along is white marbles.

3. Mrs Sharon owns a red marbles house.

4. Mr Cruz does not live at either end.

5. Mr Cruz lives somewhere to the right of the blue marbles house. 

6. Mr Danny lives in the fourth house, 

7. The first house is not made from red marbles.

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

Let's make a table of location, owner and material used for house as below and then fill up as per given details.

STEPS : 

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

1.As per clue no. 6 and 7, we have,

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

2. As per clue no.2, we have,

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

3. The clue no.3 suggests, Mrs Sharon owns a red marbles house. The only location available for this combination is second house. Hence,

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

4. The clue no.4 indicates that Mr Cruz does not live at either end. 

So, the only place that is not at the either end is house no.3 made up of white marbles. Hence, Mr. Cruz must be living at this house.

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

5. As per clue no.1, Jennifer needs to be somewhere to the left of the green marbles one. 

That green house has to be the fourth house in row and Jennifer must be living in the first house made up of blue marbles for above clue to be true.

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

The Numbered Neighbors - Puzzle

AJ, Celeste, Juan, Kara, Lily, and Randy all live on Redwood Avenue. Each of their house numbers has three digits, but the only digits in their house numbers are 2, 3, 5, and 6. The same digit may appear twice in one of the addresses.
AJ's house number is Juan's house number doubled. 

Juan lives next to Lily and right across from Randy. 

Randy's number is the lowest on the street. 

Celeste's number is a higher number than AJ's but has the same three digits as his. They both have the same digit in the hundreds place. 

Kara's house number is the reverse of Juan's. 

What is each person's street address?

View Answer! 

The Numbered Neighbors Puzzle - Solution

What was the puzzle?

As we know, AJ, Celeste, Juan, Kara, Lily, and Randy all live on Redwood Avenue. Each of their house numbers has three digits, but the only digits in their house numbers are 2, 3, 5, and 6 with repetition of digits in house number allowed. 

Let's have all the given clues once again here.

1. AJ's house number is Juan's house number doubled. 

2. Juan lives next to Lily and right across from Randy. 

3. Randy's number is the lowest on the street. 

4. Celeste's number is a higher number than AJ's but has the same three digits as his. They both have the same digit in the hundreds place.
 
5. Kara's house number is the reverse of Juan's.

STEPS : 

1] As per (1), AJ's house number is double of Juan's house number. From the given sets of digits i.e. 2, 3, 5, 6, this is only possible if there is 3 at third place of Juan's house number and 6 at third place of AJ's house number.

That is AJ's house number is XX6 and that of Juan's is XX3.

2] As we can see carry is not being forwarded from Juan's house number XX3 while getting doubled to give AJ's house number. So, it's clear that, the number formed by first two digits of AJ's house number is exactly double of the number formed by first two digits of Juan's house number.

From the given set of digits 2, 3, 5, 6, possible house numbers of AJ and Juan are 666 & 333 or 526 & 263.

If AJ is having house number 666, then as per (4), there would be no valid house number left for Celeste using digits 2, 3, 5, 6.

Therefore, AJ's house number must be 526 and that of Juan's must be 263

3] Now, as per (2), Randy must be having house number 262.

4] As per (4), Celeste's house number must be 5XX. Since, his house number has same digits as that of AJ's but higher than AJ's house number, he must be having house number 562.

5] As per (5), Kara's house number is reverse of Juan's. Therefore, Kara's house number is 362.

6] And as per (2), for the fact that Juan is living next to the Lily to be true, Lily must have house number 265 using the given set of digits 2, 3, 5, 6.

CONCLUSION :

The street addresses of all are listed as below - 

AJ         : 526, Redwood Avenue.
 
Celeste : 562, Redwood Avenue.
 
Juan     : 263, Redwood Avenue.
 
Kara     : 362, Redwood Avenue.
 
Lily       : 265, Redwood Avenue.
 
Randy   : 262, Redwood Avenue.

 

Story of Farmer's 3 Sons

A farmer’s wife made some chapatis…The farmer had 3 sons…. 

The first son came, gave one chapati to the dog,and made three equal parts of remaining chapatis, ate one part of it and left the other two parts for his brothers…. Other two sons came one after the other and did the same thinking that they came first…

Then at night all three came to the house, one of them gave one chapati to dog and made three equal parts and the three brothers ate one-one part of it… 

If no chapati was broken in pieces then how many minimum number chapatis did the mom made?

Here are MATHEMATICAL steps for solution! 

Mathematics in the Story of Farmer's 3 Sons

What was the story?

Let X be the number of chapatis that farmer's wife made.

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

First son gave 1 chapati to dog. Chapatis left = (X - 1)

Made 3 equal parts of remaining. Chapatis in each part = (X - 1)/3

He Ate one part of it. Chapatis left = 2(X - 1)/3.

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

Second son gave 1 chapati to dog. Chapatis left = 2(X - 1)/3 - 1

Made 3 equal parts of remaining. Chapatis in each part = [2(X - 1)/3 - 1]/3

He Ate one part of it. Chapatis left = 2[2(X - 1)/3 - 1]/3 

                                                  = [4(X-1) – 6]/9

                                                  = (4X - 10)/9

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

Third son gave 1 chapati to dog. Chapatis left = (4x - 10)/9 - 1

Made 3 equal parts of remaining. Chapatis in each part = [(4X - 10)/9 - 1]/3

He Ate one part of it. Chapatis left = 2[(4X - 10)/9 - 1]/3

                                                  = (8X – 20 – 18)/27 
       
                                                  = (8X – 38)/27 

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

At that night, one of them gave 1 chapati to dog.

Chapatis left = (8X – 38)/27 - 1

After that they made 3 equal parts of remaining parts and each son ate one part.

If we assume that each son ate Y chapatis then,

Y = [(8X – 38)/27 - 1]/3

Y = (8X - 38 – 27)/81

Y =  (8X – 65)/81

81Y= 8X - 65

X = (81Y + 65)/8 

X = 81Y/8 + 65/8

X = 10Y + Y/8 + 8 + 1/8

X = 10y + 8 + (y+1)/8

For X to be integer, Y has to be 7,15,23.....

So possible values of X are - 79, 160, 241.

Since, question asks minimum number, the farmer's wife must have made 79 chapatis in total.

The Mistimed Clock!

Andrea’s only timepiece is a clock that’s fixed to the wall. One day she forgets to wind it and it stops.

She travels across town to have dinner with a friend whose own clock is always correct. When she returns home, she makes a simple calculation and sets her own clock accurately.

 
How does she manage this without knowing the travel time between her house and her friend’s?


That's how she manages to set it accurately!
 

Correcting The Mistimed Clock!

 How it was mistimed?

Andrea winds her clock & sets it to the arbitrary time. Then, she leaves her house and when she reaches her friend's house, she note down the correct time accurately. Now, after having dinner, she notes down the correct time once again before leaving her friend's house.

After returning to home, she finds her own clock acted as 'timer' for her entire trip. It has counted time that she needed to reach her friend's house + time that she spent at her friend's house + time she needed to return back to home.

Since, Andrea had noted timings at which she reached & left her friend's house, she can calculate the time she spent at her friend's house. After subtracting this time duration from her unique timer count she gets the time she needed to reach to & return from her friend's house.

She must have taken the same time to travel from her home to her friend's home and her friend's home to her home. So dividing the count after subtracting 'stay time' she can get how much time she needed to return back to home.

Since, she had noted correct time when she left her friend's home, now by adding time that she needed to return back to home to that, she sets her own clock accurately with correct time.

Let's try to understand it with example.

Suppose she sets her own clock at 12:00 o' clock and leave her house. Suppose she reaches her friend's home and note down the correct time as 3:00 PM. After having dinner she leaves friend's home at 4:00 PM.

After returning back to home she finds her own clock showing say 2:00 PM. That means, she spent 120 minutes outside her home with includes time of travel to and from friends home along with time for which she spent with her friend. If time of stay at her friend is subtracted from above count, then it's clear that she needed 60 minutes to travel to & return back from friend's home.

That is, she needed 30 minutes for travel the distance between 2 homes. Since, she had noted correct time as 3:00 PM when she left friend's home, she can set her own clock accurately at 3:30 PM.

Who Lives Where?

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 ?

Know about location and home about each!

Owners Of Homes in Home Town

What were the clues? 

To simplify the process, let's number the houses as 1,2,3,4 and separate clues given.

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.

As per clues (b) and (g), 1 and 3 aren't made of red marbles. Since Danny is living in 4 as per (f), the red house owned by Mrs. Sharon must be positioned at 2.

Since 2 is already occupied, as per (d), Mr. Cruz must be living at number 3 which is of white marbles according to (b).

According to (a), 4 must be green marbles since otherwise Jennifer wouldn't be somewhere at left. As per (f) this 4 th house is owned by Mr.Danny.

The only house left for Jennifer is blue positioned at 1.

To conclude,

Mrs Jennifer - blue marbles at Number 1
Mrs Sharon - red marbles at Number 2
Mr Cruz - white marbles at Number 3
Mr Danny - green marbles at Number 4

Grandma's Birthday And Troll Toll

You are on your way to visit your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her the cakes you've made.

Between your house and her house, you have to cross 7 bridges, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake.

How many cakes do you have to leave home with to make sure that you arrive at Grandma's with exactly 2 cakes?

How many you should carry? Know here!

Source 

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.