Crossing The Stone Bridge : Puzzle

Three people, Ann, Ben and Jen want to cross a river from left bank to right bank. Another three people, Tim, Jim and Kim want to cross the same river from right bank to left bank.

However, there is no boat but only 1 stone bridge consisting of just 7 big stones(not tied to each other), each of which can hold only 1 person at a time. All these people have a limited jumping capacity, so that they can only jump to the stone immediately next to them if it is empty.
 
Now, all of these people are quite arrogant and so will never turn back once they have begun their journey. That is, they can only move forward in the direction of their destination. They are also quite selfish and will not help anybody traveling in the same direction as themselves.

But they are also practical and know that they will not be able to cross without helping each other. Each of them is willing to help a person coming from opposite direction so that they can get a path for their own journey ahead. With this help, a person can jump two stones at a time, such that if, say, Ann and Tim are occupying two adjacent stones and the stone next to Tim on the other side is empty, then Tim will help Ann in directly jumping to that stone, and vice versa.

Now initially the 6 people are lined up on the 7 stones from left to right as follows:

Ann Ben Jen emp Tim Jim Kim
(where emp stands for empty stone).

Your job is to find how they will cross over the stones such that they are finally lined up as follows:

Tim Jim Kim emp Ann Ben Jen

Now, find out the shortest step-wise procedure, assuming that Tim moves first.

THIS is the shortest way! 

Crossing The Stone Bridge Puzzle : Solution

What was the puzzle?

Initially the 6 people are lined up on the 7 stones from left to right as follows:
Ann Ben Jen EMP Tim Jim Kim
(where EMP stands for empty stone).

Step 1: Tim jumps to occupy the empty stone.

Ann Ben Jen Tim EMP Jim Kim

Step 2: Tim helps Jen in occupying the newly emptied stone between him and Jim. 

Ann Ben EMP Tim Jen Jim Kim
 
Step 3: Ben occupies the stone emptied by Jen.

Ann EMP Ben Tim Jen Jim Kim

Step 4: Ben helps Tim in occupying the newly emptied stone. 

Ann Tim Ben EMP Jen Jim Kim

Step 5: Jen helps Jim in occupying the empty stone. 

Ann Tim Ben Jim Jen EMP Kim

Step 6: Kim occupies the stone emptied by Jim. 

Ann Tim Ben Jim Jen Kim EMP

Step 7: Kim helps Jen in occupying the stone vacated by her. 

Ann Tim Ben Jim EMP Kim Jen
  
Step 8: Jim helps Ben in occupying the stone vacated by Jen. 

Ann Tim EMP Jim Ben Kim Jen

Step 9: Tim helps Ann in occupying the empty stone.

EMP Tim Ann Jim Ben Kim Jen

Step 10: Tim jumps to the stone emptied by Ann.

Tim EMP Ann Jim Ben Kim Jen

Step 11: Ann helps Jim in occupying the stone vacated by Tim.

Tim Jim Ann EMP Ben Kim Jen

Step 12: Ben helps Kim in occupying the stone vacated by Jim. 

Tim Jim Ann Kim Ben EMP Jen

Step 13: Ben occupies the empty stone.

Tim Jim Ann Kim EMP Ben Jen

Step 14: Kim helps Ann in occupying the stone emptied by Ben. 

Tim Jim EMP Kim Ann Ben Jen

Step 15: Kim jumps to the stone emptied by Ann.

Tim Jim Kim EMP Ann Ben Jen

This is exactly what we wanted!

 

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.

The Camel and Banana Puzzle

The owner of a banana plantation has a camel. He wants to transport his 3000 bananas to the market, which is located after the desert. The distance between his banana plantation and the market is about 1000 kilometer. So he decided to take his camel to carry the bananas. The camel can carry at the maximum of 1000 bananas at a time, and it eats one banana for every kilometer it travels.

What is the most bananas you can bring over to your destination?

As many as 'these' numbers of bananas can be saved!

The Camel and Banana Puzzle : Solution

What was the puzzle? 

 Let A be the starting point and B be the destination in this transportation. If the camel is taken with 1000 bananas at start, to reach the point B which is 1000 km away from A, it needs 1000 bananas. So there will be no bananas left to return back to point A.

That's why we need to break down the journey into 3 parts.

Part 1 :

For every 1 km the camel needs to -

1. Move ahead 1 km with 1000 bananas but eat 1 banana in a way.

2. Leave 998 bananas at the point and take 1 banana to return back to previous point.

3. Pick up another 1000 bananas and move forward while eating 1 banana.

4. Drop 998 bananas at the same point. Return back to previous point by consuming 1 banana.

5. Pick left over 1000 bananas and move 1km forward while consuming 1 banana to same point where 998 + 998 bananas are dropped. Now, the camel doesn't need to  return back to previous point. So, 998 + 998 + 999 are carried to the point.

That is for every 1km, the camel needs 5 bananas.

After 200 km from point A, the camel eats of 200x5 = 1000 bananas and at this point the part 1 ends.

-------------------------------------------------------------------------------------------------
 
PART 2 :

1. Move ahead 1 km with 1000 bananas but eat 1 banana in a way.

2. Leave 998 bananas at the point and take 1 banana to return back to previous point.

3. Pick up another 1000 bananas and move forward to the point where 998 bananas left while eating 1 banana.

Now, the camel needs only 3 bananas per km.

So for next 333 km, the camel eats up 333x3 = 999 bananas.

-------------------------------------------------------------------------------------------------
 
PART 3 :

So far, the camel has travelled 200 + 333 = 533 km from point A and needs to cover 1000 - 533 = 467 km more to reach at B.

Number of bananas left are 3000 - 1000 - 999 = 1001.

Now, instead of wasting another 3 bananas for next 1 km here, better drop 1 banana at the point P2 and move ahead to B with 1000 bananas. This time the camel doesn't need to go back at previous points & can move ahead straightaway.

For the remaining distance of 467 km, the camel eats up another 467 bananas and in the end 1000 - 467 = 533 bananas will be left.

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

Who Is The Engineer?

On a train, Smith, Robinson, and Jones are the fireman, the brakeman, and the engineer (not necessarily respectively). Also aboard the train are three passengers with the same names, Mr. Smith, Mr. Robinson, and Mr. Jones.

(1) Mr. Robinson is a passenger. He lives in Detroit.
(2) The brakeman lives exactly halfway between Chicago and Detroit.
(3) Mr. Jones is a passenger. He earns exactly $20,000 per year.
(4) The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.
(5) Smith is not a passenger. He beats the fireman in billiards.
(6) The passenger whose name is the same as the brakeman’s lives in Chicago.

Who is the engineer?

Want to know who? Click Here! 

That's Why Smith Is An Engineer!

Would you like to read question first? 

Let's list all the clues once again here.

(1) Mr. Robinson is a passenger. He lives in Detroit.
(2) The brakeman lives exactly halfway between Chicago and Detroit.
(3) Mr. Jones is a passenger. He earns exactly $20,000 per year.
(4) The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.
(5) Smith is not a passenger. He beats the fireman in billiards.
(6) The passenger whose name is the same as the brakeman’s lives in Chicago.

Since as per (2), the brakeman lives exactly halfway between Chicago and Detroit, locations Chicago or Detroit can't be nearest to him. Hence, the passenger that (4) is suggesting must be nearer to brakeman than Chicago and Detroit.

Now as per (1), Mr. Robinson lives in Detroit, means he is not the nearest to brakeman. Mr.Jones earning is $20,000/year as per (3), which is not evenly divisible by 3. Hence, the passenger (4) is pointing is not Mr.Jones.

So neither Mr. Robinson not Mr.Jones but Mr.Smith is the nearest neighbor. 

Now Mr. Robinson lives in Detroit and Mr.Smith is living in between Chicago and Detroit but nearer to brakeman. Hence, Mr. Jones must be living in Chicago.

According to (6), Jones must be name of the brakeman as he is sharing his name with the man living in Chicago.

And if Smith is not fireman as per (5), he must be an engineer!   

  

Abnormal Looking Normal Puzzle

A donkey travels the exact same distance daily. Strangely 2 of his legs

travels 40 kilometers and the remaining two travels 41 kilometers. 

Obviously 2 donkey legs cannot be a 1km ahead of the other 2.

The donkey is perfectly normal. So how come this be true ?

 I'm perfectly normal!

Why so? Find it here! 

Source 

That Looks Perfectly Normal

What was looking abnormal? 

The donkey is moving on a circular path. Hence, his 2 legs on right (or left depending on moving clockwise or anticlockwise) moves along a circle having lesser radius than circle on which left legs are moving. The difference in circumferences of circles accounts the difference in distance traveled.