Maze Challenge For a Rat?

A rat is placed at the beginning of a maze and must make it to the end. There are four paths at the start that he has an equal chance of taking: path A takes 5 minutes and leads to the end, path B takes 8 minutes and leads to the start, path C takes 3 minutes and leads to the end, and path D takes 2 minutes and leads to the start.

What is the expected amount of time it will take for the rat to finish the maze?

This could be the average time that rat needed!
 

A Rat Finishing off The Maze!

The challenge ahead of rat?

For rat, there are 2 paths viz A (5 minutes) and C (3 minutes) leading to the end while paths B (8 minutes) and D (2 minutes) lead to the start again.

Since, there are 4 paths & each having equal chance of being chosen by rat, there is 1/4 th chance for each path for to be chosen by rat.

Let's assume T be the time needed for rat to finish the maze. 

But if rat selects path B or D then rat need T more time again as these paths lead to the start of the maze again.

Hence,

T = (1/4) x A + (1/4) x B + (1/4) x C + (1/4) x D

T =  (1/4) x 5 + (1/4) x (8 + T) + (1/4) x 3 + (1/4) x (2 + T)

T = (5/4) + (2) + (T/4) + (3/4) + (1/2) + (T/4)

T =  (9/2) + (T/2)

T/2 = 9/2

T = 9

That is rat needs 9 minutes to finish the maze. 

 

Puzzle : Set Timer without Clock?

You are a cook in a remote area with no clocks or other way of keeping time other than a four-minute and a seven-minute hourglass. On the stove is a pot of boiling water. Jill asks you to cook a nine-minute egg in exactly 9 minutes, and you know she is a perfectionist and can tell if you undercook or overcook the egg by even a few seconds. 

How can you cook the egg for exactly 9 minutes?

You should follow THIS process! 

Solution : Setting up Timer without Clock!

What was the challenge?

We can set up a timer of 9 minutes using 4 and 7 minutes hourglass. Below is the process-

1. Flip both the hourglasses and drop egg into the water. 

2. After 4 minutes, 4-minutes hourglass will run out. Flip and reset it. ( 4 minutes counted and 3 minutes countdown left in 7-minute hourglass).

3. After 3 minutes, the 7-minutes hourglass will run out while 1 minute countdown will be left in 4-minutes hourglass. ( So far 4 + 3 = 7 minutes counted ). 

Flip the 7-minutes hourglass thereby resetting it's timer.

4. After 1 minute, the 4-minutes hourglass will run out. ( 4 + 3 + 1 = 8 minutes counted). 

5. At this point of time there will be sand for 6 minutes countdown left in 7-minutes hourglass. Just flip it so that it count exactly 1 more minute.
   

Now, that's how 4 + 3 + 1 + 1 = 9 minutes are counted.

 

"Hear & Identify What the Time is!"

Your grandma’s wall clock chimes the appropriate number of times at every whole hour, and also once every 15 minutes. If you hear the wall clock chime once, how much more time do you need to figure out what the time is, without looking at it?

This is the way to figure out the exact time!

Source 

The Count Will Tell The Exact Time!

What was the challenge?

Since the clock chimes appropriate number of times at every whole hour, it's not difficult to predict the exact time after counting sounds but the exception of 1:00 AM/PM.

For example, if the first sound you heard at 4:30 AM then you will hear another sound at 4:45 AM and clock will strike 5 times at 5 AM by which you will easily know the exact time. So, even if you heard it at 15 minutes past any hour, you will need only 45 minutes to figure out the exact time.

But at 1:00 AM/PM the clock will strike only once & there the problem starts.

In worst condition, if you have heard first sound at 12:15 then clock will strike once for next 6 times at 12:30, 12:45, 1:00, 1:15, 1:30, 1:45. That is you will hear clock strike once for 7 consecutive times. So in worst condition, you need 1 hour and 30 minutes to figure out the exact time.


And if you hear the single strike for less than 7 consecutive times, then you can easily figure out the exact time.

 

Breaking The Safe in 5 Minutes?

Charlie Croker and his team need to break the safe to finish a secret job named "Italian Job" in exactly a five minutes.

They got just one chance and five minutes to finish the job else the local police will be informed.

He got following clues

1st Clue: Exactly one number is perfectly placed.
9 2 5

2nd clue: Everything is incorrect.
9 3 8

3rd clue: Two numbers are part of the code of the safe, but are wrongly placed.
4 9 6

4th clue: One number is part of the code of the safe, but is wrongly placed.
5 8 1

5th clue: One number is part of the code of the safe, but is wrongly placed.
1 2 6 

This should be the process!

To Break The Safe in 5 Minutes...

What was the challenge? 

Re listing all the clues...

1st Clue: Exactly one number is perfectly placed.
9 2 5

2nd clue: Everything is incorrect.
9 3 8

3rd clue: Two numbers are part of the code of the safe, but are wrongly placed.
4 9 6

4th clue: One number is part of the code of the safe, but is wrongly placed.
5 8 1

5th clue: One number is part of the code of the safe, but is wrongly placed.
1 2 6 

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From 2nd clue, it's clear that 9,3,8 are not part of the code.

Hence correct number suggested by 1st clue must be 2 or 5

Since 9 is not part of the code, the other 2 correct numbers that 3rd clue pointing must be 4 and 6.

If 6 is the part of code, then 1 & 2 are not as 5th clue is suggesting.

And since 2 isn't part of the code then 1st clue must be pointing 5 is correct digit placed in right position.

The 4th clue is also suggesting that 5 is the part of the code but not 1 or 8.

If 5 is correct at it's position as per first clue then 4 and 6 must be occupying other 2 places.

As per 3rd clue position of 4 is wrong, it must be at second place and hence 6 at first place.

Hence the code is 645!

Burn The Strings

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is constant and strings are identical.

How do you measure 45 minutes?

That's how to measure 45 minutes!

Timer Using Burning Strings

What was the challenge? 

1. Burn both the ends of 1st string and 1 end of other string.

2. After 30 minutes, 1st string will be burnt out and half of the other string will be burnt out.So far we have counted 30 minutes.

3. Now burn the other end of 2nd end. It will take 15 minute to burnt out totally. This way, we have counted 30 + 15 = 45 minutes using 2 strings.