PUZZLES

#1)Measure exactly 2 liters of water if you have:


1) 4 and 5-liter bowls
2) 4 and 3-liter bowls




answer


fill 5L using 4L
fill 5L again using 4L so 3L remains in 4L
empty 5L and fill 3L in 4L
now 5L has 3L filled
so using 4L fill remain 2L
so 4L will remain with 2L

#2)The Puzzle: When asked about his birthday, a man said:

"The day before yesterday I was only 25 and next year I will turn 28."

This is true only one day in a year - when was he born?








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The Solution . . .

He was born on December 31st and spoke about it on January 1st.

#3)How can you add eight 8's to get the number 1,000? (only use addition)

The Solution . . .

The key is to this riddle is realizing that the ones place must be zero. 888 +88 +8 +8 +8 =1,000 

 

#4)TWO TRAIN PUZZLE

Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h. A fly starting out at the front of one train, flies towards the other at a speed of 75 km/h. Upon reaching the other train, the fly turns around and continues towards the first train. How many kilometers does the fly travel before getting squashed in the collision of the two trains?
Now, the trains take one hour to collide (their relative speed is 100 km/h and they are 100 km apart initially). Since the fly is traveling at 75 km/h and flies continuously until it is squashed (which it is to be supposed occurs a split second before the two oncoming trains squash one another), it must therefore travel 75 km in the hour's time. The position of the fly at time is plotted above.
However, a brute force method instead solves for the position of the fly along each traversal between the trains. For example, the fly reaches the second train when

(1)

or h, at which point it has traveled a distance km. It then turns around and reaches the first train again when

(2)

or . Continuing, the total distance traveled by the fly is given by summing the series

(3)

When posed with a variant of this question involving a fly and two bicycles, John von Neumann is reputed to have immediately answered with the correct result. When subsequently asked if he had heard the short-cut solution, he answered no, that his immediate answer had been a result of explicitly summing the series (MacRae 1992, p. 10; Borwein and Bailey 2003, p. 42).


#5)Sequence of numbers Puzzle:

Question:
Sequence of numbers
1 11 21 1211 111221
What will be the next one in the above sequence?

Solution:
It is a strange sequence. Each number describes the resemblance of the previous one, except the first one.
11 describes the previous '1' which contains one '1'
21 describes the previous '11' which contains two '1'
1211 describes the previous '21' which contains one '2' and one '1'
111221 describes the previous '1211' which contains one '1', one '2' and two '1'.
So the next sequence will be 312211, that is the previous '111221' contains three '1', two '2' and one '1'.


#6) Midas has boxes in three sizes: large, medium, and small. He puts 11 large boxes on a table. He leaves some of these boxes empty, and in all the other boxes he puts 8 medium boxes. He leaves some of these medium boxes empty, and in all the other medium boxes he puts 8 (empty) small boxes. Now, 102 of all the boxes on the table are empty.
How many boxes has Midas used in total?

The Solution . . .

By putting 8 boxes in a box, the total number of empty boxes increases by 8-1 = 7.
If we call x the number of times that 8 boxes have been put in a box, we know that 11 + 7x = 102. It follows that x=13. In total, 11 + 13 × 8 = 115 boxes have been used.




#7)Book
From a book, a number of consecutive pages are missing. The sum of the page numbers of these pages is 9808.
Which pages are missing?

The Solution . . .

Let the number of missing pages be n and the first missing page p+1.
Then the pages p+1 up to and including p+n are missing, and n times the average of the numbers of the missing pages must be equal to 9808:
n(((p+1)+(p+n))/2)=9808
In other words:
n*(2*p+n+1)/2=2*2*2*2*613
So:
n*(2*p+n+1)= 2*2*2*2*2*613
One of the two terms n and 2*p+n+1 must be even, and the other one must be odd. Moreover, the term n must be smaller than the term 2*p+n+1.It follows that there are only two solutions:
n=1 and 2*(p+n+1)=2*2*2*2*2*613, so n=1 and p=9808, so only page 9808 is missing.
n=2*2*2*2*2 and 2*p+n+1=613, so n=32 and p=290, so the pages 291 up to and including 322 are missing.
Because it is asked which pages (plural) are missing, the solution is: the pages 291 up to and including 322 are missing.







#8)Light Bulb Puzzle:

Question:
A light bulb is hanging in the first floor of the room. There are three switches in the ground floor room. One of these switches belongs to that light bulb. The light bulb is not lit and the switches are in off state. There is only one chance to visit the room. How can it be determined which of these switch is connected to the light bulb.


 
 Solution:

First turn ON the first switch and leave it for few minutes. Then turn OFF the first switch and ON the second switch. Now enter the first floor room. If the light bulb is lit, the second switch must be connected to it. If it is not lit, it might the first or the third switch. Now touch the light bulb, it is hot it will be the connected to the first switch. Nor if it is cold, then it should be the third one.