"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!

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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.

 

Arrange Positions Around The Round-Table

King Arthur and his eleven honorable knights must sit on a round-table. In how many ways can you arrange the group, if no honorable knight can sit between two older honorable knights?

Here are the possible combinations!

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Possible Positions Around The Round Table

What was the challenge?

If king K is sitting at the center then the youngest knight must sit to right or left of the king i.e. 2 possible positions for him.

The second youngest knight now can sit either left or right of the group of 2 made above.

The third youngest knight now can sit either left or right of the group of 3 made above.

And so on.

That is every knight has 2 possible positions except the oldest knight who will have only 1 position left.

This will be make sure each of the knight (except youngest one) has at least 1 younger neighbor (youngest one has king as one neighbor).

So after putting youngest in 2 possible ways the next youngest can be put another 2 possible ways. That is 4 possible combinations for 2.

Similarly, for arranging 3 knights' positions there can be 2^3 = 8 possible combinations.

This way for 10 knights (excluding the oldest which will have only 1 seat available at the end) there are 2^10 = 1024 possible combinations.

Sharing The Driving Time!

John and Mary drive from Westville to Eastville. John drives the first 40 miles, and Mary drives the rest of the way. That afternoon they return by the same route, with John driving the first leg and Mary driving the last 50 miles.

Who drives the farthest, and by what distance?

'This' is the person who drives the farthest!


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Uneven Sharing of Driving Time!

But actual how it was shared?

Let's assume for a moment, the distance between Westville and Eastville is 50 miles.

In this case, John drives only 40 miles while Mary drives 10 + 50 = 60 miles. For any distance beyond 50 miles, Mary drives east equal distance as John drives west.

So in any case the difference will remain same of 20 miles. So Mary drives the farthest by 20 miles.

What is Color of His Hat?

There is a basket full of hats. 3 of them are white and 2 of them are black. There are 3 men Tom, Tim, and Jim. They each take a hat out of the basket and put it on their heads without seeing the hat they selected or the hats the other men selected.

The men arrange themselves so Tom can see Tim and Jim’s hats, Tim can see Jim’s hat, and Jim can’t see anyone’s hat.

Tom is asked what color his hat is and he says he doesn’t know.

Tim is asked the same question, and he also doesn’t know.

Finally, Jim is asked the question, and he does know.

What color is his hat?

Know color of his hat!