#91 - Hard Mathematical Logic Puzzle

A devotee visits 9 temples when he visits India. All these nine temples have one thing in common - there are 100 steps in every temple. The devotee puts Re.1 coin after climbing up every step. He does the same while climbing down every step. At each temple, the devotee offers half of his money from his pocket to god. In this way, his pocket becomes empty after his visit to 9th temple.

Can you calculate the total amount he had initially ?

Hard Mathematical Logic Puzzle

146900

In such cases, we calculate from the last thing. Thus in this case, let us start counting from the 9th temple. Since, he must have offered 100 coins while climbing down stairs, it means that he must have offered Rs. 100 to god on the ninth temple and offered Rs. 100 while climbing up steps. Thus it is clear that he had Rs. 300 in his pocket before climbing the steps of the 9th temple.

Similarly, we will calculate for all the temples backwards.
Before eight temple: (300+100)*2 + 100 = 900
Before seventh temple: (900+100)*2 + 100 = 2100
Before Sixth temple: (2100+100)*2 + 100 = 4300
Before fifth temple: (4300+100)*2 + 100 = 8900
Before fourth temple: (8900+100)*2 + 100 = 18100
Before third temple: (18100+100)*2 + 100 = 36,500
Before second temple: (36500+100)*2 + 100 = 73300
Before first temple: (73300+100)*2 + 100 = 146900

Therefore he had Rs. 146900 initially.

#92 - Maths Tricky Problem

If you remove one from eleven, it becomes ten. If you remove one from nine, it becomes ten.

How is this possible ?

Maths Tricky Problem

It is possible if you are using Roman Numerals.
9 = IX
10 = X
11 = XI
Now it is all possible.

#93 - Trivia Maths FAQ Riddle

Given the numbers between 1 and 1 million, what is so special about the number 40 that it makes the number stand out of the crowd ?

Trivia Maths FAQ Riddle

The number 40 (Forty) is the only number which when written in English has all the letters in the same order as in the alphabets.

#94 - IAS Tricky Logical Question

You board a train. The train will have to enter a tunnel soon. You are claustrophobic. Which place is the best for you to sit ?

IAS Tricky Logical Question

The back seat of the last coach will be the best. The reason is because, the train will be accelerating after the stop and thus, it will be much faster when the back of the train enters the tunnel than when the front of the train enters. Thus you will have to spend less time in the tunnel.

#95 - Tricky Number Sequence Puzzle

Analyze and find the missing item in the sequence:
16, 06, 68, 88, __, 98

Tricky Number Sequence Puzzle

L8

This is a bit tricky questions. To solve you must look at the series upside down. It is actually
91, 90, 89, 88, __, 86

So we need 87 in the place of blank. To achieve 87 in an upside down position, the correct answer will be L8.

Thus, the missing item in the series is L8.

#96 - Fun Probability Question

Upon tossing a fair coin ten times, you get heads every time.
What is the probability that in the next toss, it will land with heads up again?

Fun Probability Question

50%

The next toss of the coin is not dependent upon the previous ten tosses. Thus, the probability is 50 percent only.

#97 - Mystery Number Riddle

Consider all the numbers between 1 and 1 million. Among all these numbers, there is something very special about the number 8 and the number 2202. What is it ?

Mystery Number Riddle

If you start arranging the numbers alphabetically, the numbers 8 (eight) will come first and the number 2202 (two thousand two hundred and two) will come at last.

#98 - Cricket Riddle

How many runs at maximum can a batsman score in a normal one day match? Consider the fact that the conditions are ideal and there are no No Balls, no Wide Balls and no Extras in that match.

Cricket Riddle

If we are considering an ideal case and we have to calculate the maximum score, we will assume that the batsman hits six on every ball. But then, at the end of every over, the strike will change. But we have to make sure, he gets to play maximum number of balls to score maximum runs. Thus, the batsman will hit six in first five balls and will choose to take 3 runs in the last ball so that he retains the strike in the following over.

Total runs per over in that case = 6 * 5 + 3 = 33.

But in the last over (50th over), he don’t have to worry about keeping the strike and thus, he will hit six even on the last ball. Therefore, the maximum runs that a batsman can score:

33 * 49 + 6 * 6 = 1617 + 36 = 1653

#99 - What Word Am I Thinking Of Riddle

I am an eleven letter word.
The first, second, third and fourth letter combine to form a bankquot;s name.
The fifth, sixth and seventh letter combine to form a carquot;s name.
The eighth, ninth, tenth and eleventh letter combine to form a mode of transport.

Can you identify what word am I?

What Word Am I Thinking Of Riddle

CITIZENSHIP

#100 - Hard Conditional Probability Problem

Four friends - Anna, Brian, Christy and Drake are asked to choose any number between 1 and 5.

Can you calculate the probability that any of them chose the same number ?

Hard Conditional Probability Problem

Let us take this one step at a time.

Let us calculate the probability that Anna and Brian have the same number in their mind.
101/125

Now, there's a 1/5 chance that the numbers will be same and 4/5 chance that the numbers are different.

Let us now include Christy in this data. There can be two cases.
1) Anna and Brian have the same number. In that case, Christy will have only one number to compare.
2) Anna and Brian did not have the same number. In that case, Christy will have two numbers to compare to.

For the first case, the probability will be 5/25. This is if Anna and Brian did have the same numbers.

But if Anna and Brian did not have the same numbers, there is a 2/5 probability that Christy is having the same number (this is because Christy gets to match her number with both Anna and Brian). In that case, we can simply multiply the probabilities.
4/5 * 2/5 = 8/25

Otherwise, if Christy is not having the same number, the probability is 3/5. Now multiplying with the previous chain:
4/5 * 3/5 = 12/25

Now, we can include Drake in our calculations. If we follow the path where Drake's number matches with Anna and Brian, the probability will be 25/125.

Now let us join that with Christy's probability. If Christy's number matches with Anna and Brian and Drakes' number also matches, then the probability will be:
4/5 * 2/5 = 40/125

If Christy's number does not match with Anna and Brian but Drake's number matches with Christy's, the probability will be:
4/5 * 3/5 * 3/5 = 36/125

But if Christy's number does not matches with Anna and Brian and even Drake's does not matches with Christy, then the probability will be:
4/5 * 3/5 * 2/5 = 24/125

Now, we have to tell the probability when all the four friends have same numbers, so we will just add up the probability where all the numbers matches:

25/125 + 40/125 + 36/125 = 101/125.