Interesting Facts

Following is a dozen of puzzles that I found very interesting. Try to solve them.

1. A man is condemned to death. He is given to say a last statement; if it is truth
he is hanged to death and if it is false he is poisoned. He uttered his last sentence from which he escaped. What is the last statement ?


2. In a 3 way junction there is a house in which there are 2 brothers. Elder one always tell the TRUTH and the younger one alway LIE. Here a man comes from one road and wanted to go for a particular city (say city A) and he don't know which way to take out of the two. He knows that in that house there are 2 brothers who always made TRUE and FALSE statements but he donot know who is who. At one time there is one one brother at home. The traveller asks only one question from one of the brothers who is there at that moment and chooses the correct way for his destination. What is that question and whats the road he chooses ?


3. A,B,C are aligned according to their height. A the shortest. C the tallest. A, B,C are faced left. They cannot see back. C can see A&Bs' head. B can see only A's head and A cannot see anybody's head. After C there is D who holds a gun. ie they stand like A B C D(with the gun)
D has 3 white hats and 2 black hats
ABC are blind fold and hats are put onto their head. After that,
Now C can see A&B's hat colors,
B can see A's hat color

Now respectively C,B,As' chance to predict the color of the hat that they are wearing (one at a time starting with C). If someone made a mistake he will be shot to death(by D). A,B,C are intelligent and try to escape from the death.
They all can hear previous guy's answer and if the previous guy is shot to death the sound of gun fire.
This is what happend.
First C uttered the answer, but shot to death.
Then B uttered the answer, but again shot to death.
Finnally A uttered the answer and it is the correct answer
So he escaped from the death.

What is the answer and explain
how A thought(actually you) that it is the color of
A's hat.



4. You are given two threads which takes 1hr to burn from one end to the other. Using these 2 threads and a matchbox(or lighter) how will you measure 45 minutes You are not allowed to break these threads.


5. A warden of a prison comes back to the prison from a party very drunk. Inhis state, he accidentally turns the key to open all 100 of the jail cells.He realizes what he's done, so he goes back and turns the key on every othercell (thus, now cell 1 is open, cell 2 is closed, cell three is open, etc.).He realizes that he hasn't closed all of them, so he goes back and turns thekey on every third cell (thus, now cell 3 is closed, and cell 6, which heclosed when he turned every other key, is now open). Still drunk, he goesback and turns the key on every 4th, then every 5th, 6th, 7th, etc. until heturns the key on every 100th cell (thus, only on cell #100). After all this,which cells remain open?

6. There are 4 people that need to cross a bridge. Only two can go across at a time and one has to come back with the flashlight each time. They take 1 minute, 2 minutes, 4 minutes and 5 minutes. They only walk as fast as the slowest one. They are able to all cross the bridge in 12 minutes. How?


Very good one

7. Pretend you have two strings which burn at random rates but which will alwaysbe completely burned in exactly one hour. Thus, after 1/2 hour the stringswill NOT necessarily be half burned length-wise, only time wise. How do you use these strings to time exactly 45 minutes without using any othertime-keeping device?
It is inaccurate to assume that each 4th of string A will burn in exactly 15 minutes. Three of the fourths could take one minute, and the other could takea full hour (thus, the entire string burns in one hour, as said).
The string, remember, burns at random rates in random places. If you were tocut it into four pieces and light each SEPARATELY so that one would beginburning when another stopped, the sum of the time would be one hour. That isall you can assume. For example, if you lit all of them together, three ofthe fourths could burn in exactly one minute, and the last fourth could take57 minutes. Thus the entire string burns in one hour. That is the onlyassumption you can make. You must look a little beyond just the string.


8. There are 3 settlers and 3 indians on one side of the creek. How can you get them all over to the other side by using a boat that holds two(they can only get there by boat). You can never have more indians than settlers on one side at a time because the indianswill kill the settler.


9. You ask a person to pick a number. Say they pick the number 20, 20 has six lettres in it, so therefore 20 is 6, then you see that 6 has three lettre's in it, so 6 is 3, 3 has five lettres so, 3 is 5, 5 has four lettre's so 5 is 4, and four is cosmic. this pattern works for any number, at all. so quickly, take the number 13 (thirteen), 13 is 8 (eight), 8 is 5 (five), 5 is four and four is cosmic.

10. Three men, members of a safari, are captured by cannibals in the jungle. The men are given one chance to escape with their lives. The men are lined up and bound to stakes such that one man can see the backs of the other two, the middle man can see the back of the front man, and the front man can't see anybody. The men are shown five hats, three of which are black and two of which are white. Then the men are blindfolded, and one of the five hats is placed on each man's head. The remaining two hats are hidden away. The blindfolds are removed. The men are told that if just one of the men can guess what hat he's wearing, they may all go free. Time passes. Finally, the front man, who can't see anyone, correctly guesses the color of his hat. What color was it, and how did he guess correctly?

11. Ten men stand in a line facing same direction.
Random Red or White hat is placed on their head(one hat per person).
One cannot see his own color(of the hat) but can see everybody else's in front of him.
The first man(Man1) cannot see anybody else's whereas the last man(Man10) can see 9hats.
They know ten men got 10 hats but we do not know how many Reds or Whites were there.
The game organizer starts asking men from the last in line(Man10, Man9,... Man2, Man1)
the color of individual's own hat.
When a man gives correct answer he is awarded a one point.
Individual's answers is heard by everybody else in the line. Their correctness exposed at the end.
What is the strategy the group should take to maximize their group score.
Hint : They can get 9 points.

12. X number of cards are placed on table A. Out of X, Y number of them are face down.
You have to move cards (one at a time) from table A to table B.
After the move both tables should have equal number of cards face down.
You are blind folded and sit in the middle of tableA and tableB.
(means you can touch the cards but you cannot see whether they are face up or down)
You are given the values of X and Y.
How do you accomplish this ?


ANSWERS

1."I should be poisoned" think a bit and analyse. Still if you don't get keep on reading.
Explanation : If "I should be poisoned" is TRUE(by sentense) you have to poison him. But according to the rule of the riddle "He should be hanged". Because of the contradiction no one can hang him or poison him. This solves by CONTRADICTION.

2. "If your brother is here instead of you what would he say for the question "What is the correct way to city A" ? " Then he chooses the other road whatever the brother say.

3.A cannot be black, because if A was black, C or B
would live.
If C sees A is black:
if C sees B is also black
then he knows he is white, and lives.
Cannot happen.
else C sees B is white
B knows this because if he were black
and A were black, C would live.
No matter how C answers, B has to be white, if A
is black, or C would live.

Therefore A cannot be black, and has to be white for
both C and B to die.

4.Burn both ends of one thread and one end of the other. After the first thread is burnt completely burn the other end of the second thread. The total time taken by threads to burn will be 45 minutes.


5. All the cells that are perfect squares (1,4,9,16,25,36,49,64,81,100)remain open because they have an odd number of multiples so the key will be turned an odd number of times on them, making them open at the end. Allothers have an even number of multiples and will stay closed.

6. 1&2 : 2mins, 1back : 1min, 4&5 : 5mins, 2back : 2mins, 1&2 : 2mins = 12mins

7. The first thing you must understand is that the time which it takes the strings to burn is proportional to the number of flames present on the string. If you light both ends of one of the strings, it will take HALF of an hour to burn, by definition. Thus, to time 45 minutes, here's what you'd do. Light string A at both ends while you simultaneously light string Bon one end. When string A is completely burned up, 30 minutes will have passed. At the moment that this happens, you will have 30 minutes left on string B. Right as string A burns out, light the OTHER end of string B, which will now only burn for 15 more minutes because you have two flames on a30-minute string. When it's gone, 45 minutes total have passed.

8. Any number could be ended in four which always has four letters only.

9.This is similar to the priest devil game that I had preciously posted.
Check the first comment of that game or play the game to find the solution.
http://24x7interestingfacts.blogspot.com/2008/09/priests-n-devils.html

10. If black is 1 and white is 0
All possible combinations :
a. 000
b. 001
c. 010
d. 011
e. 100
f. 101
g. 110
h. 111

a. does not happen ; if e fist buy can answer
if c or g, second guy could have answered
In all other cases 3rd guy wears black.

11. If one sees odd number of (say) Reds he calls RED. Then the one in front

12. Pick a card from tableA , flip the side and place on tableB
You do this until you reach Y.

Hope you enjoyed the puzzles!