The Water Jug Challenge : Puzzle

You've got a 4 liter jug and a 9 liter jug. 

You've got a pool of water. 

What is the fewest number of steps it takes to come up with exactly 6 liters of water? 

No, you cannot pour some water into the 9 liter jug and then guess. Nor can you fill each jug up half way or something. You have to be exact. A step is defined as putting water into a jug (not emptying). For instance, filling the 4 liter jug and then pouring it into the 9 liter jug is 2 steps.

Click here for SOLUTION! 

The Water Jug Challenge Puzzle : Solution

What was the puzzle?

We've got a 4 liter jug and a 9 liter jug. 

We've got a pool of water. 

We have to find fewest number of steps it takes to come up with exactly 6 liters of water. 

STEPS : 

1. Fill up the 9 liter jug from the pool.         9L - 9  4L - 0

2. Fill up the 4 liter jug from the 9 liter jug. 9L - 5  4L - 4

3. Empty the 4 liter jug into the pool.          9L - 5  4L - 0

4. Fill 4 liter jug again from the 9 liter jug.   9L - 1  4L - 4

5. Empty the 4 liter jug into the pool           9L - 1  4L - 0

6. Transfer 1 liter left 9L jug into the 4L.     9L - 0  4L - 1

7. Fill the 9 liter jug from the pool.             9L - 9  4L - 1

8. Fill up the 4 liter jug from the 9 liter jug. 9L - 6  4L - 4

That's how we have exactly 6 liters of water in 9 liters jug. 

Walking Up An Ascending Escalator

My wife and I walk up an ascending escalator. I climb 20 steps and reach the top in 60 seconds. My wife climbs 16 steps and reaches the top in 72 seconds. If the escalator broke tomorrow, how many steps would we have to climb?

Here is way to find the total number of steps! 

Total Steps on Broken Escalator

What was the question?

Climbing 16 steps makes you to reach at the top in 72 seconds but if you climb 20 steps then it requires 60 seconds only.

That means, climbing 4 steps extra pushes you at the top saving 12 seconds. This is the speed of the escalator which is 4 steps per 12 seconds.

That is escalator speed is 1 step per 3 seconds and 20 steps per 60 seconds. But in 60 seconds I climb 20 steps more hence total steps on escalator must be 40.

This is how escalator pushes me 20 steps + I climb 20 steps = 40 steps in 60 seconds.

On the other hand my wife climb 16 steps + escalator pushes her (40-16) i.e. 24 steps = 40 steps in 72 seconds.  


MATHEMATICAL APPROACH :

Let's suppose there are 'x' steps on escalator. If M is my speed , W is my wife's speed and E is speed of the escalator in terms of steps per second then,

M = 20/60 = 1/3 and W = 16/72 = 2/9.

In my case, for relative speed (steps per second) x/60, we have,

M - E = x/60

1/3 - E = x/60    ...........(1)

And in my wife's case, for relative speed (steps per second) x/72, we have, 
 
W - E = x/72

2/9 - E = x/72  ..............(2)

Subtracting (2) from (1),

(1/3) - (2/9) = (x/60) - (x/72)

(1/9) = x / 360

X = 40

So there are 40 steps on the escalator. 

Generous Devotee

A devotee visits 9 temples when he visits India. All these nine temples have one thing in common - there are 100 steps in every temple. The devotee puts Re.1 coin after climbing up every step. He does the same while climbing down every step. At each temple, the devotee offers half of his money from his pocket to god. In this way, his pocket becomes empty after his visit to 9th temple.

Can you calculate the total amount he had initially ? 

Click here to know exact amount! 

Donations By The Devotee

Why to calculate those?

Using algebraic equations in the case can make things complicated unnecessarily. Hence, we would start from backward. Before putting 100 coins on steps while climbing down 9th temple devotee must had 100 coins. That means he had 200 coins when he climbed up the 9th temple half of which i.e. 100 he offered to that temple & 100 put on the 100 steps of 9th temple. Moreover, he must have placed 100 coins while climbing up 9th temple. So before visit to 9th temple he must had, (100 x 2) + 100 = 300 coins.

Same way, finding the amount he had before visit to each temple like below.

Before eight temple: (300+100)*2 + 100 = 900
Before seventh temple: (900+100)*2 + 100 = 2100
Before Sixth temple: (2100+100)*2 + 100 = 4300
Before fifth temple: (4300+100)*2 + 100 = 8900
Before fourth temple: (8900+100)*2 + 100 = 18100
Before third temple: (18100+100)*2 + 100 = 36,500
Before second temple: (36500+100)*2 + 100 = 73300
Before first temple: (73300+100)*2 + 100 = 146900

 
To conclude,  he had Rs. 146900 initially.