Winner Deserving The Scholarship

This is my favorite puzzle which I had read in a newspaper. It really makes you to think more & more logically to get the answer. I had posted it back in July but re posting it here.

"The scholarship will be awarded," said the head to three candidates - Chuckles, Wombat & Breeze - "to the winner in this little competition. I am going to chalk a cross, which will be either a green or a red cross. I shall then ask each one who can see a green cross to hold his hand up; and take his hand down as soon as he can tell me what his own cross is. He must, of course, be able to explain how his answer is arrived at. Kindly close your eyes for 10 seconds."

He chalked a green cross on all three foreheads. "Go!"

All three hands shot up in air ; that of Chuckles was almost immediately lowered. "My cross is green , Sir"

How did Chuckle know?
  
Read here how the story unfolds!



 

Popular Missing Square Puzzle

How many number of times you have come across this image?

By now, you might have accepted the solution.

"The hypotenuse is bulged in bottom figure which accounts area equal to missing square!"

But is this really a solution to this puzzle? The issue illustrated in clear manner here!

And my opinion is here!

And how creator did manage to create that 'missing' square is illustrated here!

 

"Thanks,You're Fired!"

A man is leaving on a business trip and stops by his office on the way to the airport. The night watchman stops him and says, "Sir, don't take that flight. I had a dream last night that your plane would crash and everyone would die!" The business man cancels his trip and sure enough, the plane crashes, killing all the passengers. The man gives his watchman a $10,000 reward for saving his life, then fires him. Why?

That's why! 

Source 

This Is Not Allowed On Duty

What exactly happened? 

The man awarded $10000 obviously for saving his life. The duty of night watchman is to keep watch on office at night not to sleep & dream.

That's why he fires the watchman.

Snail Up The Wall

A snail creeps 10 feet up a wall during the daytime, then falls asleep. It wakes up the next morning and discovers it slipped down 6 feet. If this happens each day, how many days will it take to reach the top of a 20 feet wall?

Escape to answer! 

Source 

A Snail On Top of The Wall !

Read the question first! 

Let's find out progress of snail day by day.

Day 1 : UP to 10, DOWN to 4

Day 2 : UP to 14, DOWN to 8

Day 3 : UP to 18, DOWN to 12

Day 4 : UP to 22 which is greater than 20.

So snail requires 4 days to reach the top of the wall.

Location Of Rabbit!

What was the task?

Zoom 
 

           

Did You Find Rabbit?

Find the rabbit

I found it here!  

How Missing Square Puzzle Created?

That's how it was missed! 

Slope of diagonal must be 5/13 = 0.385

If we keep heights of red & green triangles constant as 3 & 2 respectively

then their bases should have been.

5/13 = 3/Base of red triangle 

Base of red triangle = 7.8

And,
 

Base of green triangle = 13 - 7.8 = 5.2

Creator of this optical illusion cleverly restricted 5.2 to 5 & extended 7.8 to 8.

Or we can say he altered heights of those triangles by keeping bases 8 & 5.

Now creator shuffles those colored blocks like shown below.

Missing square puzzle

Pink & Blue rectangles shuffled diagonally. Purple rectangle of size 15 

colored blocks is replaced by orange rectangle of size 16. Obviously orange

rectangle would have 1 white block & 15 colored blocks!

 

Missing square puzzle

   
                Area of colored region in top triangle = 0.5 x 13 x 5 = 32.5 Blocks

While in bottom triangle, 

Area of colored region + White Block = 0.5 x 13 x 5 =32.5 Blocks

Missing square puzzle

 Figured out here!  

How it is created? 

  

Source 

Origin of Missing Square Puzzle

First view this! 

Actually the diagonal drawn here isn't a true diagonal.....It's slope must be 5/13 = 0.385.

Two hypotenuses (of two triangles) have different slopes; red one having 3/8 = 0.375 &
green one has 2/5 = 0.4.

So both together can't form true diagonal of this rectangle neither hypotenuse of colored triangle.

So we need to calculate area of each colored shape differently & then add to get area of colored region.

Area of colored region = 12 + 5 + 15 = 32..... Not 32.5

So if it was halved by perfect diagonal then 32.5 - 32 = 0.5 of area would have been painted more.

This is half of that white space.This is also reason why non painted part of top rectangle covers area 12 + 5 + 16 = 33 i.e. 0.5 than expected 32.5 because of imperfect diagonal.

And if we calculate area of other part (non painted) of bottom rectangle as 12 +5 +15  = 32 ; again less by 0.5 if there was perfect diagonal.

Since it is not a perfect diagonal that white space is 'missing' 0.5 of colored area & 0.5 of white space is 'taken' from other part of rectangle.

That's why 1 white space there!

Cheryl's Birthday

CAN YOU CRACK THIS MATHS OLYMPIAD QUESTION?

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.

May 15	May 16	May 19
June 17	June 18
July 14	July 16
August 14	August 15	August 17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.

Bernard: At first I don't know when Cheryl's birthday is, but I know now.

Albert: Then I also know when Cheryl's birthday is.

So when is Cheryl's birthday?

Cheryl's Birthday

CRACKED HERE!

Source 

Simplified answer to Cheryl's birthday

Wait! Here is the question!  

Possible months are May, June, July & August & possible dates are 14,15,16,17,18,

19.

Days 18 & 19 appears only once in the list. If Cheryl had told Bernard any of these

numbers then he would have came to know her exact birthday straightaway. That

would also make first part of  Bernard's statement (At first I don't know when 

Cheryl's birthday is) false. So May 19 & June 18 eliminated right away.

Had Cheryl told Albert month May or June then his statement would have been like -

Albert - 'I don't know whether Bernard knows or doesn't know when Cheryl's birthday. 

He might know her birthday if Cheryl have told him number 18 or 19. 

Or he may be unaware of exact date if Cheryl have told him numbers 15,16 or 17'.

So with months May & June, Albert is not sure whether Bernard know or doesn't know

exact date. But here Albert assured with that the Bernard too doesn't know exact date. 

Hence these two months also eliminated. 

As Albert is saying Bernard too doesn't know exact date, he is indirectly suggesting 

Bernard that month is not May or June. 

From rest of list, number 14 appears twice - once with July & once with August. 

Now from Bernard's statement he knows the exact date now. 

If it was 14, then Bernard would have been uncertain with exact month(whether it is  

July or August. So Cheryl must have told him number 15,16 or 17. 

Now what Albert is saying in his next statement is that now he too know exact date.

If Cheryl had told month August then Albert wouldn't have an idea of exact date as

August has two possibilities i.e. August 15 or August 17.  

Only date left is JULY 16 & That is Cheryl's birthday ! 

Note - For the logic behind the answer, thanks to Wikipedia.For simplification say

thanks to person named below! 

Story Of Genius Winning Scholarship

First read here what was the test?

One day Chuckles came to my home; he is my friend. I am 'smart' enough to immediately ask him story behind that mind teaser. What he had thought at that time is in his own words here...

"If I had red cross on my forehead then there is no way Wombat & Breeze raised their hand looking at me. What Wombat (or Breeze) would have thought in that case

Wombat (or Breeze) must have thought that Breeze (or Wombat) must have raised hand after looking green cross on my forehead as Chuckles have red cross on forehead.

So both would have come to know what they have on their own forehead & would have taken hands down immediately. But they didn't.

Hence I concluded, I must have green cross on my forehead & hence I took my hand down & earned the scholarship."

Genius

 *NOTES* : 

1.It's only because Chuckles is winner of competition he visited my home. Otherwise Wombat or Breeze could be my friend either.

2.All the above characters, scenes & incidents are fictitious & created just for the simplicity. A (very) little help has been taken from the Google.

Real Test Of Genius

"The scholarship will be awarded," said the head to three candidates - Chuckles, Wombat & Breeze - "to the winner in this little competition. I am going to chalk a cross, which will be either a green or a red cross. I shall then ask each one who can see a green cross to hold his hand up; and take his hand down as soon as he can tell me what his own cross is. He must, of course, be able to explain how his answer is arrived at. Kindly close your eyes for 10 seconds."

Professor

He chalked a green cross on all three foreheads. "Go!"

All three hands shot up in air ; that of Chuckles was almost immediately lowered. "My cross is green , Sir" 

How did Chuckles know?

Here it is how!