#91 - Confusing Probability Puzzle

You along with your friend are standing in front of two houses. Each of those houses inhabits a family with two children.

Your friend tells you the below two facts:
1) On your left is a family that has a boy who likes accounts but the other child loves science.
2) On the right is a family with a seven year old boy and a new born baby.

You ask him, "Does either of the family have a girl?"

To this he replies, "I am not quite sure. But can you guess that? If you are right, I will give you $200."

Which family do you think is likely to have a girl ?

1/2

In the house on the left, there are three possibilities:
Younger Older
Girl Boy
Boy Girl
Boy Boy

We cant have a girl-girl option because it has been mentioned that there is at least one boy in that house. Now all these outcomes are equally likely, and we have two events with girls, the chances of having a girl in the left house is 2/3.

In the house on the right, there are two possibilities because we already know that the older child is a boy:
Younger Older
Girl Boy
Boy Boy
Here the chances are 1/2.

Thus you must choose the house on the left for better chances at winning.

#92 - Hard Tricky Maths Trivia Question

Can you think of three numbers that gives a prime number as their product and also the difference between the second and first is equal to the difference between third and second?

The three numbers are: -3, -1 and 1.
Remember that we never asked for positive numbers.

#93 - Complete The Equation Puzzle

Below, you can see three complete equations and one incomplete. Based on the three complete ones, can you complete the incomplete one?

5 $ 4 $ 3 $ 9 = 4215
6 $ 9 $ 2 $ 6 = 3816
4 $ 7 $ 3 $ 3 = 1122
7 $ 2 $ 7 $ 4 = ____

2418 is the answer.

The algo that has been used here is

A $ B $ C $ D = [first digit of (A * D)] [last digit of (B * C)] [first digit of (B * C)] [last digit of (A * D)]

Using the same algo,
7 $ 2 $ 7 $ 4 = [first digit of (7 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (7 * 4)]
= 2418

#94 - Six Digit Number Puzzle

Calculate a six digit number that is smaller than 500000 such that the sum of its digits is 43 exactly.

499849

Let us begin with the maximum sum of a digit under 500000. Of course it will be the sum of 499999.
4 + 9 + 9 + 9 + 9 + 9 = 49.

Now, the required number must be close to it.
Rooting 499999, we get 707.106
Taking the square of 707, we get 499849.
4 + 9 + 9 + 8 + 4 + 9 = 43

Thus, the required number is 499849.

#95 - Trick Time Riddle

Doctor advised his patient to take a tablet after every fifteen minutes. He gave him five tablets in total.

How much time will he take to have all the five tablets ?

60

The patient will be able to take all the tablets in an hour. This is because the first tablet will start the time.
1st tablet = 0 min
2nd tablet = 15 min
3rd tablet = 30 min
4th tablet = 45 min
5th tablet = 60 min

#96 - Cost Pen Cap Puzzle

A pen along with its cap costs Rs. 5.50. If the cost of pen is Rs. 5, more than the cap, can you calculate the cost of the cap ?

Let the cost of cap = c
Cost of pen = (5 + c)

As per the condition

5.50 = 5 + c + c
2c = 0.5
C = 0.25

Thus the cost of the cap is 25 Paise

#97 - Trivia Number Riddle

A special integer exists in mathematics that shows a special property. If you subtract any number from that integer, the result will always be divisible by the successor of that number completely.

Do you know what that integer is ?

The required integer is -1.

For an example, let us subtract 7 from -1.

-1 - 7 = -8

Now the successor of 7 is 8 and (-8) is exactly divisible by 8.

You can try that for any number and it will hold true.

#98 - Compare Quantity Puzzle

Suppose "s" represents the number of seconds in a day and "h" represents the number of hours in ten years (which will also include two leap years), can you calculate which quantity is greater from the two variables?

S = 60 * 60 * 24 seconds = 86, 400 seconds.
H = (8 * 365 *24) + (2 * 366 *24) hours = 87, 648 hours

Clearly, H is greater than S even though not by much.

#99 - How Many Burgers Maths Problem

If one and a half boys, eat one and a half burgers in one and a half hours.

How many burgers can 9 boys eat in 3 hours ?

18

More hours => more burgers.
More boys => more burgers.

The time become twice (3 hours / 1.5 hours).
Boys become six times (9 / 1.5).

Number of burgers = 2 * 6 * Original(1.5)
= 18

#100 - Drive Time Maths Puzzle

Alpha and Beta have same amount of petrol in their respective cars. Alpha can drive for 4 hours whereas Beta can drive for 5 hours with the amount of petrol left.

Both of them start driving at the same time. After a few hours, they find out that the amount of petrol remaining in one of the cars is four times the other car.

Can you calculate for how long did they drive the cars?

3 3/4 hours

Assume that the initial amount of petrol in each of the petrol tanks be P.
Now, let us assume that they drove for H hours.

In that case, the amount of petrol used by one car in H hours will be = P*H /4
The amount of petrol used by the other car will be = P*H/5

Therefore, the petrol left in one car = P - P*H / 4
Petrol left in the other car = P - P*H / 5

Now, according to the question,
P - P*H / 5 = 4 (P - P*H / 4)
=> H = 15 / 4 = 3 3/4 hours.