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
You are given 16 witch hats. The hats are divided in four different colors – red, blue, green and yellow. Every color has been assigned to four hats. Now each of the hat will be glued with a label of an arithmetic sign – ‘+’, ‘-‘, ‘x’ or ‘/’. But you can label one sign only once on one color. In such an arrangement, the hats can be uniquely defined by its color and symbol.
Can you arrange all the 16 hats in a 4x4 grid in a fashion that no two rows and columns have a repetition of color or sign?
We have arranged four hats in the below picture to assist you.
Y B R G
G R B Y
B Y G R
R G Y B
x + - /
- / x +
/ - + x
+ x / -
Dwayne Johnson was running away with the loot from a heist in his car along with Vin Diesel. One tire was punctured and he dropped down to replace it. While changing the wheel, he dropped the four nuts that were holding the wheel and they fell into a drain. Vin Diesel gave him an idea using which they were able to drive till the rendezvous point.
What was the idea ?
Vin Diesel told him to use one nut from each of the other wheels.
A man was gazing through the window of the 33rd floor of the building. He suddenly opened the window and jumped on the other side of the window. On landing the floor, there was not a sheer mark of injury on him.
How can that be possible if he did not use any kind of parachute and did not land on a soft surface ?
The man is a window cleaner who jumped inside of the window after finishing off on the 33rd floor.
Vin Diesel is pulling a theft and has planned to run away with all the cash kept in the safe. But the only way to open the safe is the 13 character password. He has a set of five clues given to him by a trustworthy source.
Exactly two of the below statements are false.
The password is contained within this sentence.
The password is not in this hint.
The password is within only one of these statements.
At least one of the above statement is a lie.
The Password, Clues 2 and 5 are correct and rest are lies.
There are 100 bulbs in a room. 100 strangers have been accumulated in the adjacent room. The first one goes and lights up every bulb. The second one goes and switches off all the even numbered bulbs - second, fourth, sixth... and so on. The third one goes and reverses the current position of every third bulb (third, sixth, ninth… and so on.) i.e. if the bulb is lit, he switches it off and if the bulb is off, he switches it on. All the 100 strangers progresses in the similar fashion.
After the last person has done what he wanted, which bulbs will be lit and which ones will be switched off ?
Ponder over the bulb number 56, people will visit it for every divisor it has. So 56 has 1 & 56, 2 & 28, 4 & 14, 7 & 8. So on pass 1, the 1st person will light the bulb; pass 2, 2nd one will switch it off; pass 4, light it; pass 7, switch it off; pass 8, light it; pass 14, switch it off; pass 28, light it; pass 56, switch it off.
For each pair of divisors the bulb will just end up back in its preliminary state. But there are cases in which the pair of divisor has similar number for example bulb number 16. 16 has the divisors 1 & 16, 2 & 8, 4&4. But 4 is recurring because 16 is a perfect square, so you will only visit bulb number 16, on pass 1, 2, 4, 8 and 16… leaving it lit at the end. So only perfect square bulbs will be lit at the end.
13 caves are arranged in a circle at the temple of doom. One of these caves has the treasure of gems and wealth. Each day the treasure keepers can move the treasure to an adjacent cave or can keep it in the same cave. Every day two treasure seekers visit the place and have enough time to enter any two caves of their choice.
How do the treasure seekers ensure that they find the treasure in minimum possible days ?
If one of the treasure seeker moves clockwise every day and one of the treasure seeker moves anti clockwise, they will find the treasure in minimum seven days.
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
Find the next number in the series ?
1 10 24 43 67 ?
96
Difference between two numbers are
9,14,19,24,29.
Difference between every consecutive number is 5.
So next number is 67+29=96
