#251 - Mathematical Rebus Riddle
What does the below mathematical rebus means ?
For a change
#252 - Tricky Math Logic Problem
A girl was fond of collecting rare stamps. When she was twenty years old, she bought a box to collect her stamps. On her every birthday, she put 250 stamps in it and her sister who was also fond of collecting stamps took out 50 stamps from it on her birthday. The girl met an accident when she was 60 years old. When her box was opened, there were only 500 stamps in it.
How is it possible logically?
The girl was born on 29 February, thus she put 250 stamps every four years.
In forty years, she put stamps only 10 times which makes the total of 2500 stamps.
Her sister was born on any other day and she took out 50 stamps from the box forty times which makes the total stamp she took out to be 2000.
Thus after forty years, the girl’s box had only 500 stamps.
#254 - 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.
#255 - Maths Logical Problem
Accidentally, two trains are running in the opposite direction and enter a tunnel that is 200 miles long. A supersonic bird that has fled the lab and taken shelter in the tunnel starts flying from one train towards the other at a speed of 1000 mph. As soon as it reaches the second train, he starts flying back to avoid collision and meets the first train again at the other end. The bird keeps flying to and fro till the trains collide with each other.
What is the total distance that the supersonic bird has traveled till the trains collided?
Let us consider the length of the tunnel first; which is 200 miles. Now, the trains are running on the same speed which means that they will collide at the center of the tunnel and will take an hour to reach the center. Now the bird is travelling at a speed of 1000 mph and it is flying for an hour (since the trains will take an hour to collide). Thus the bird will travel 1000 miles in the process.
#256 - Challenging Math Equations Puzzle
We have arranged an array of numbers below. What you have to do is use any kind of mathematical symbol you know excluding any symbol that contains a number like cube root. You can use any amount of symbols but you have to come up with a valid equation for all of them.
0 0 0 = 6
1 1 1 = 6
2 + 2 + 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6
(0! + 0! + 0!)! = 6
(1 + 1 + 1)! = 6
2 + 2 + 2 = 6
3 x 3 - 3 = 6
√4 + √4 + √4 = 6
5 + 5/5 = 6
6 + 6 - 6 = 6
7 - 7/7 = 6
8 - √√(8 + 8) = 6
√(9 x 9) - √9 = 6
#257 - Math Brain Twister
100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 = ?
Since you can notice that there are fifty pairs of n^2 - (n-1) ^2,
n^2 - (n-1)^2 = n + (n - 1)
Thus 100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 can also be written as
100 + 99 + 98+ ... + 2 + 1 = (100 x 101)/2 = 5050
#258 - Maths Brain Twister Puzzle
A research team went to a village somewhere between the jungles of Africa. Luckily for them, they reached on the day when quite an interesting custom was to be performed. The custom was performed once in a year as they confirmed and was performed in order to collect the taxes from every male of the region.
The taxes were to be paid in the form of grains. Everyone must pay pounds of grain equaling his respective age. Which means a 20 year old will have to pay 20 pounds of grains and a 30 years old will pay 30 pounds of grain and so on.
The chief who collects the tax have 7 weights and a large 2 pan scale to weigh. But there is another custom that the chief can weigh only with three of the seven weights.
Can you find out the weights of the seven weights? Also what is the maximum age of the man that can be weighed for the payment of taxes ?
There is a thing which you must keep in mind. The chief can put weights on both the pans.
Keeping that in mind
The weights 1, 3, 7, 12, 43, 76, 102
The oldest age that can be measured with these weights is 122
#259 - Maths Picture Area Puzzle
The below figure consists of a rectangle and the numbers labeled over the top represents the area of that particular shaded region.
Calculate the area of the green region labeled as '?'
The White triangle is similar to the Red triangle
As ratio of areas = ratio of bases when height is same,
Ratio of sides is 2:3
White triangle = 9/4 * Red triangle = 9/2
Thus the Green Region = 5.5 units.
#260 - Smart Maths Bet Puzzle
Two friends were betting. One said to the other, “The coin will be flipped twenty times and each time the coin lands on head, I will give you $2 and each time it lands on tale, you will give me $3.†After flipping the coin for twenty times not a single penny was exchanged among them.
How many times did the coin land on heads ?
12
Let x be the number of time heads appeared
2x = 3(20-x) --- this is because the amount won and lost was equal
X=12