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.

 

Who is older, Joe or Smoe?

Two friends, Joe and Smoe, were born in May, one in 1932, the other a year later. Each had an antique grandfather clock of which he was extremely proud. Both of the clocks worked fairly well considering their age, but one clock gained ten seconds per hour while the other one lost ten seconds per hour. 

On a day in January, the two friends set both clocks correctly at 12:00 noon. "Do you realize," asked Joe, "that the next time both of our clocks will show exactly the same time will be on your 47th birthday?" Smoe agreed. 

Who is older, Joe or Smoe?

Know who is older in the case! 

"Smoe is older than Joe"

What was the puzzle?

Since one of the clock looses and other gains 10 seconds per hour, that means one looses 240 seconds (4 minutes) & other gains 240 seconds (4 minutes) in a day.

Both the clocks are set at 12:00 PM correctly. One has to gain 6 hours (360 minutes) and other has to loose 6 hours (360 minutes) to show the same time again. At the speed of 4 minutes per day the would need 360/4 = 90 days to show the same time again. 

On 90th day, they will come together to show 6:00. Exactly at 12 noon on 90th day one clock must be showing 6:00 PM and other must be showing 6:00 AM, if they have feature of showing AM/PM.

Now as per Joe it would be 47th birthday of Smoe on the day on which the clocks will show the same time. That means, the clocks are set correctly on the noon of 90 days prior to Smoe's birthday which is 1 May for sure but year yet to be known. 

If the year is leap year then 90th day before 1st May will be on 1st February and if it's not a leap year then it would be on January 31. Since, they have set their clocks correctly at 12:00 on some day in January, the year must not be a leap year. 

But if Smoe had been born in 1933, his 47th birthday would have been on May 1, 1980 which is leap year. Hence, Smoe must have born in 1932 and Joe in 1933.

Therefore, Smoe is older than Joe.

The story must be of 1979!

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.

"Save Your House From Me!"

Okay, I’ll ask three questions, and if you miss one I get your house. Fair enough? Here we go:

1.A clock strikes six in 5 seconds. How long does it take to strike twelve?

2.A bottle and its cork together cost $1.10. The bottle costs a dollar more than the cork. How much does the bottle cost?

3.A train leaves New York for Chicago at 90 mph. At the same time, a bus leaves Chicago for New York at 50 mph. Which is farther from New York when they meet?

You need little common sense in answering above!

Presence of Common Sense in Answers!

What where questions?

1. A clock strikes six in 5 seconds. How long does it take to strike twelve?

A: Not 10 seconds, it takes 11 seconds.

Here, interval between 2 strikes is 1 second i.e. if counter started at first strike, it will count 1 second after second strike, 2 seconds after third strike & so on. 

Hence, 11 seconds needed for strike 12.

2.A bottle and its cork together cost $1.10. The bottle costs a dollar more than the cork. How much does the bottle cost?

A: Not 1 dollar, it would cost $1.05.

If x is cost of cork,
x + (x +1) = 1.10
2x = 0.10
x = 0.05

Hence cost of bottle is $1.05 and cost of cork is $0.05



3.A train leaves New York for Chicago at 90 mph. At the same time, a bus leaves Chicago for New York at 50 mph. Which is farther from New York when they meet?

A: Obviously, when they meet at some point then that point must be at the some distance from New York. Hence, they are at the same distance from the city.

Tricky Logical Mathematical Puzzle

Can you solve this?

 
Do you too think answer is 19 or 26 ? Here is the right one!

Answer of Tricky Logical Mathematical Puzzle

Or a look at the question itself?


Let's look at the puzzle once again.

From first equation, it is clear that figure = 15. But the figure itself made up of square (4 sides) + polygon (5 sides) + hexagon (6 sides) = 15.

From second equation, we have bunch of 4 bananas = 4 i.e. 1 banana = 1.

And from third equation, we have 3 hours in clock = 3 i.e. 1 hours  = 1.

Hence, in fourth equation, value of clock = 2, 3 bananas = 3, figure = sides of hexagon + sides of pentagons = 6 + 5 = 11.

2 + 3 + 3 x 11 = 38

Hence, answer is 38. 

Losing Ten Minutes An Hour

A clock loses exactly ten minutes every hour. If the clock is set correctly at noon, what is the correct time when the clock reads 3:00pm?

Faulty Clock

Find it here!

Source 

Real Time Of a Faulty Clock

How much faulty it was? 

A clock loses 10 minutes in every hour that means for 60 real minutes it shows 50 minutes. In another words, real time is 60/50 = 1.2 times the minutes shown by the slower clock. It was set correctly at noon & at 3:00 PM ; 180 minutes of slower clock elapsed. That means the real time is 180 x 1.2 = 216. So it's 3:36 PM in real time clock!

Correct Time