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How it Will Affect the Water Level?

A man stuck in a small sailboat on a perfectly calm lake throws a stone overboard. It sinks to the bottom of the lake.

When the water again settles to a perfect calm, is the water level in the lake higher, lower, or in the same place compared to where it was before the stone was cast in?


How it Will Affect the Water Level?


Did you think it will rise? 

Physics : Finding the Effect on the Water Level


But why water level was affected?

Do you recall what does Archimedes Principle state? For an object to float on water, it has to displace that much volume of water whose weight is equal to weight of the object itself. Now if object has less density than water then obviously it has to displace lesser amount of volume of water to float on it. That means it has to sink less in water.

For a moment, let's assume the stone has very high density & hence having weight equal to hundreds of kilograms despite of having small volume.

Here, stone sinks to the bottom of the lake suggests that it is has more density than water. It can't displace the water whose weight is equal to it's weight.But when it was on sailboat it could push the sailboat down so that more water is displaced weighing equal to it's weight. Result of this, the sailboat sinks little 'deeper' compared to when stone wasn't there.

Obviously, the volume of displaced water when stone was in sailboat (due to stone only) must be greater that the volume of displaced water when stone sinks to the bottom of the lake. That's why both sailboat and stone together could float on the water. In short, sailboat helped stone to displace amount of water needed to float which results in rise in shoreline.

And when stone is thrown out of the sailboat, then ideally it can't displace more water than when it was on sailboat. Now, sailboat sinks less 'deeper' in water displacing only water need to float itself. 



Physics : Finding the Effect on the Water Level


That's why the water level must be dropped compared to earlier. The little rise due to water displaced by stone can't exceed the earlier water level for the reason explained above.



"Square,Square; Which Color?"

A square tabletop measures 3n × 3n. Each unit square is either red or blue. Each red square that doesn’t lie at the edge of the table has exactly five blue squares among its eight neighbors. Each blue square that doesn’t lie at the edge of the table has exactly four red squares among its eight neighbors. How many squares of each color make up the tabletop?


"Square,Square; Which Color?"


Here is correct way to count those!

Counting Colorful Squares!


How squares are arranged?

The tabletop measures 3n × 3n, so we can divide it evenly into n2 ( 3 × 3) squares that together tile the surface completely.

Let's consider a piece of square of size 3 x 3. For each such unit of 3 x 3 -

1. If the center of the square is red square, then there are 5 blue squares and 3 red squares surrounded with it. 

Counting Colorful Squares!


2. If the center is blue square, then there are 4 blue and 4 red squares surrounding that square. 

Counting Colorful Squares!

In any case, for 3 x 3 = 9 squares, there are 5 blue and 4 red squares. 

Therefore, for tabletop of 3n x 3n, there will be 5n2 blue squares and 4n2 red squares.  

Challenge of Inverted Playing Cards

One fine day, Mr. Puzzle and Mr. Fry were playing cards, but suddenly power went off and they were getting bored. So Mr. Puzzle randomly inverted position of 15 cards out of 52 cards(and shuffled it) and asked Mr. Fry to divide the card in two pile with equal number of inverted cards (number of cards in each pile need not be equal).

It was very dark in the room and Mr. Fry could not see the cards, after thinking a bit Mr. Fry divided the cards in two piles and quite surprisingly on counting number of inverted cards in both the piles were equal.

Challenge of Inverted Playing Cards

What do you think Mr. Fry must have done?


This is what he must have done! 

  

Equating Counts of Inverted Cards in Piles


What was the challenge?

Mr.Fry must have taken top 15 cards & inverted positions of all. So he divides deck into 2 piles - one with 15 cards & other 37 cards.

Now suppose if there are 7 cards that were inverted in top 15 & 8 were inverted in remaining 37. When he flips top 15, 7 remains in normal position & 8 remains in inverted position. That is equal to 8 cards in inverted position from pile of 37 cards.

In short, if there are N cards inverted in top 15 then there are  15 - N cards inverted in remaining 37 cards. So on flipping position of top 15, there will be 15 - N cards in inverted position in top 15. That's how both piles would have equal number of inverted cards i.e. 15-N.  

Equating Counts of Inverted Cars in Piles
 

Had Mr.Puzzle inverted positions of 20 cards randomly then Mr. Fry would have flipped top 20 cards. He would have made 2 piles with one with 20 cards & other 32 cards to equate the count of inverted cards in piles.

Escape Story of 3 Robbers!

Three robbers, Babylas, Hilary, and Sosthenes, are stealing a treasure chest from the top of an old tower. Unfortunately, they’ve had to destroy their ladder to avoid pursuit, so they’ll have to descend using a crude tackle — a single pulley and a long rope with a basket at each end.

Babylas weighs 170 pounds, Hilary 100 pounds, Sosthenes 80 pounds, and the treasure 60 pounds. If the difference in weight between the two baskets is greater than 20 pounds then the heavier basket will descend too quickly and injure its occupant (though the treasure chest can withstand this). 

How can the three of them safely escape the tower with the treasure?

Escape Story of 3 Robbers!


That's how they escape!


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