How will you represent (3AC)14 in base 7 numeral system.

It can be done using this formula!
If a no X is represented in base 14 as
X = an a(n-1) a(n-2) .... a(0)

then in base 7 we can write it as

X=.....rqp

where
p=(2^0)a(0)%7;
q=((2^1)a(1) + p/7)%7
r=((2^2)a(2) + q/7)%7
..........
nth term=((2^n)a(n) + (n-1)th term/7)%7
(will go further because a no. in base 14 will require more digits in base 7).

The logic is simple, just based on properties of bases, and taking into account the fact that 7 is half of 14. Else it would have been a tedious task.

Eg. here it is given 3AC.
C =12;
so last digit is (2^0 * 12)%7 = 5
A=10
next digit is (2^1 * 10 + 12/7)%7 = (20+1)%7=21%7=0
next is 3;
next digit is (2^2 * 3 + 21/7)%7 = (12+3)%7=15%7=1
next is nothing(0);
next digit is (2^3 * 0 + 15/7)%7 = (0+2)%7=2%7=2

Hence, in base 7 number will be, 2105.

Now try how you can perform any base to any other base conversion ?

You are given n dice. Each die has m sides i.e has values from 1 to m. Given m,n,x calculate the probability that the sum of all the dice is greater than or equal to x.

Example  n=4 m=2 x=8 ans: 1/16=0.0625  n=2 m=6 x=3 ans:35/36=0.972

You are given two hourglasses. One measures 4 minutes and one measures 7 minutes. How would you measure exactly 9 minutes?

Step	Time	4 minute timer	7 minute timer
1	0 min	Start	Start
2	4 mins	Flip	3 minutes left
3	7 mins	1 minute left	Flip
4	8 mins	Stop	Flip (1 minute left)
5	9 mins		Stop

You have 50 red marbles and 50 blue marbles. Your have two jars. If I am to choose a jar at random, what ratios of marbles would you put in each jar to increase the probability of me choosing a red marble?

Determine which jar has the heavier marbles in the least amount of weighings

You have 10 jars .Each jar has 100 marbles
9 of the 10 jars -> each marble weighs 1 gram each
last jar -> each marble weights 1.1 grams each
electronic weight scale
    - place what you want to weight on it
    - hit a button
    - get the total weight

find the defective jar ?

Answer:Take 1 marble from jar 1, 2 from jar 2, 3 from jar 3 and so on...so u have 55 marbles in all
Weigh them all together...if total weight is 55.1....then jar 1 is the one with obese marbles...if 55.2..then jar 2...and so on...  again 55.3 can't be the combination of jar 1 and 2 as (.1 +.2 ) since defective jar is only one.

Three Doors, 1 Prize Puzzle , One of Toughest Puzzle on Probabality

You are on a gameshow and the host shows you three doors. Behind one door is a suitcase with $1 million in it, and behind the other two doors are sacks of coal. The host tells you to choose a door, and that the prize behind that door will be yours to keep.
You point to one of the three doors. The host says, "Before we open the door you pointed to, I am going to open one of the other doors." He points to one of the other doors, and it swings open, revealing a sack of coal behind it.
"Now I will give you a choice," the host tells you. "You can either stick with the door you originally chose, or you can choose to switch to the other unopened door."
Should you switch doors, stick with your original choice, or does it not matter?

Einstein's Riddle

ALBERT EINSTEIN'S RIDDLE ARE YOU IN THE TOP 2% OF INTELLIGENT PEOPLE IN THE WORLD? SOLVE THE RIDDLE AND FIND OUT.


There are no tricks, just pure logic, so good luck and don't give up.

1. In a street there are five houses, painted five different colors.

2. In each house lives a person of different nationality

3. These five homeowners each drink a different kind of beverage, smoke different brand of cigar and keep a different pet.  

THE QUESTION: WHO OWNS THE FISH?

HINTS

   1. The British man lives in a red house.
   2. The Swedish man keeps dogs as pets.
   3. The Danish man drinks tea.
   4. The Green house is next to, and on the left of the White house.
   5. The owner of the Green house drinks coffee.
   6. The person who smokes Pall Mall rears birds.
   7. The owner of the Yellow house smokes Dunhill.
   8. The man living in the center house drinks milk.
   9. The Norwegian lives in the first house.
   10. The man who smokes Blends lives next to the one who keeps cats.
   11. The man who keeps horses lives next to the man who smokes Dunhill.
   12. The man who smokes Blue Master drinks beer.
   13. The German smokes Prince.
   14. The Norwegian lives next to the blue house.
   15. The Blends smoker lives next to the one who drinks water.

ALBERT EINSTEIN WROTE THIS RIDDLE EARLY DURING THE 19th CENTURY. HE SAID THAT 98% OF THE WORLD POPULATION WOULD NOT BE ABLE TO SOLVE IT.  

Feel free to comment your answers and share to your friends.