### #1 - Hour Glass Riddle

You have two hour glasses one measure 7 minutes and other measure 4 minutes.
Using these two hour glasses, you need to measure exactly 9 minutes.

How come ?

Step1 : Start running both the hourglasses.
Step2 : when 4 minutes hourglass runs out, turn it over.
Step2 : when 7 minutes hourglass runs out, turn it over.
Step2 : Again when 4 minutes hourglass runs out, turn 7 minute hourglass over (it was running for exactly one minute.)
Step2 : 8 minute already passed and allow one minute of 7 hour glass to get over. ==>9 minute

### #2 - Challenging Puzzle

Outside a room there are three light switches. One of switch is connected to a light bulb inside the room.
Each of the three switches can be either 'ON' or 'OFF'.

You are allowed to set each switch the way you want it and then enter the room(note: you can enter the room only once)

Your task is to then determine which switch controls the bulb ??

Set the first switches on for abt 10min, and then switch on the second switch and then enter the room.
Three cases are possible
1.Bulb is on => second switch is the ans
2.Bulb is off and on touching bulb , you will find bulb to be warm
=>1st switch is the ans.
3.Bulb is off and on touching second bulb , you will find bulb to be normal(not warm)
=>3rd bulb is the ans.

### #3 - Oracle Probability Interview Question

What is the probability of choosing the correct answer at random from the options below.

a) 1/4
b) 1/2
c) 1
d) 1/4

If the answer is 1/4, then because 2 out of 4 answer choices are '1/4', the answer must actually be 1/2. This is a contradiction. So the answer cannot be 1/4.
If the answer is 1/2 (or 1), then because 1/2 (or 1) is 1 out of 4 answer choices, the answer must be 1/4. This is again a contradiction. So the answer cannot be 1/2 (nor 1).

So none of the provided answer choices are correct. Therefore the probability of choosing the correct answer is 0%

### #4 - Cross Bridge Puzzle

Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

17 mins

The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 mins. Is that it? No. That would make this question too simple even as a warm up question.

Let’s brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let’s put all this together.

1 and 2 go cross
2 comes back
7 and 10 go across
1 comes back
1 and 2 go across (done)

Total time = 2 + 2 + 10 + 1 + 2 = 17 mins

### #5 - Tricky Logic Puzzle

I have some blue and red sock in my drawer.
I have total of 4 socks.
I pick 2 socks and chances that i get pair of red socks is 1/2.

What is the chance of picking a pair of blue socks ?

zero

I had 3 red socks and 1 blue sock.

=> chances of pair of red socks = 1/2
chances of pair of mixed socks = 1/2
chances of pair of red socks = NULL

### #6 - Knockout Tournament Matches Puzzle

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 15 matches are played in total, how many players participated?
(b) If 50 players took part in the tournament, how many matches were played?

(a) If you look at the question closely, it is a knockout tournament and the winner will be just one. Thus no. of players is equal to 15+1=16.
(b) The number of matches will always be one less than the number of players (in knockout tournaments). Thus the answer is 49.

### #7 - Tough Probability Interview Question

There is a country where everyone wants a boy. Every family continue to have babies till a boy is born. If the probability of having a girl or a boy is the same, what is the proportion of boys to girls after some time in that country?

Since the probability of having a girl or a boy is same, half of the families will have a boy first and stop. The other half of the families will have a girl and from half of those families, the second born will be a boy and they will stop while the others will again have a girl. This process will continue.

Suppose the number of couples are N, the number of boys will be N.

1/2 have a boy and stop: 0 girls
1/4 have a girl, then a boy: N/4 girls
1/8 have 2 girls, then a boy: 2*N/8 girls
1/16 have 3 girls, then a boy: 3*N/16 girls
1/32 have 4 girls, then a boy: 4*N/32 girls

Total: N boys and
1N 2N 3N 4N
– + – + – + — +… = ~N

Therefore the proportion of boys to girl will be quite close to 1:1.

### #8 - Maths Logic Riddle

It can be easily calculated that the digits 0 to 9 can be arranged into 3628800 distinct ten digit numbers.

But i also knowns how many of these numbers are prime.

Do you ?

Zero

The sum of numbers from zero to nine is 45 and can be divisible by 3 and 9.

### #9 - Logical Thinking Riddle

I have 100 coins in my wallet.

What is the minimum number of coin(s), i would be required in order to make sure each coin touched exactly three other coins.

4

3 placed flat on the table in a triangle(touching each other) and put the fourth one on top of them in the middle.

### #10 - Water Pails Puzzle

If you had an infinite supply of water and a 5 quart and 3 quart pails, how would you measure exactly 4 quarts? and What is the least number of steps you need?

1. Fill 5 quarter pill ( 5p - 5, 3p - 0)
2. Transfer to 3 quart pail (5p - 2, 3p - 3)
3. Empty 3 quarter pill ( 5p - 2, 3p - 0)
4. Transfer 2q from 5 pail to 3 pail (5p - 0, 3p - 2)
5. Fill 5 quarter pail(5p - 5, 3p - 2)
6. Transfer 1q from 5 pail to 3 pail(5p - 4, 3p - 3)