In the attached figure, you can see a chessboard and two rooks placed on the chess board. What you have to find is the number of squares that do not contain the rooks.How many are there?
128
Lets count them one by one.
62 squares of size 1x1.
41 squares of size 2x2.
18 squares of size 3x3.
6 squares of size 4x4.
1 square of size 5x5.
62 + 41 + 18 + 6 + 1 = 128 squares.
You have an empty wine bottle (too bad eh?) with a cork that has been secured at the top in a normal way. There is a metal ring inside the bottle that is suspended by a string.
How can you make the metal ring drop to the bottom if you are not allowed to touch anything - not the bottle, not the cork, not the thread and not the ring?
You just need a magnifying glass to do considering you are out in open with bright sun rays available to you. With the glass, you can burn through the string and thus making the ring drop to the bottom.
At a certain point of time someone observes a clock and find out that the hour hand is exactly at the minute mark and the minute hand is six minutes ahead it. The clock is observed again to find out that hour hand is exactly on a different minute mark but the minute hand is seven minutes ahead of it this time.
Can you calculate the time that has elapsed between the two observations?
two hours and twelve minutes.
If you know about clocks, you must be knowing the fact that the hour hand is exactly on the minute mark five times each hour i.e. on the hour, twelve minutes past the hour, twenty four minutes past the hour, thirty six minutes past the hour and forty eight minutes past the hour.
Now let us suppose that X are the number of hours and Y are the number of minutes past the hour.
When the hour hand is on minute mark,
Position of hour hand:
5X + Y/12
Position of the minute hand:
Y
Now when the first observation is taken,
Y = Y = 5X + Y/12 + 6
This is also equivalent to 60X = 11Y - 72.
But from what we know, Y can only be equal to 0, 12, 24, 36 or 48. Thus keeping that in mind, the only value possible for X and Y are 1 and 12 respectively. This implies that the time is 1:12 on the first observation.
In the second observation, the equation will be:
60X = 11Y - 84
The possible values for X and Y here are 3 and 24 respectively. This implies that the time is 3:24.
Now time that has elapsed between 1:12 and 3:24 = two hours and twelve minutes.
Can you find out a way through which you can make five squares out of the given figure by moving just six match sticks?
Many of you might have tried making five different squares but that was not asked in the question. See the figure for the explanation.
There was a blind beggar living on the footpath of a street. Suddenly on day, the beggars brother died. What was the relation of the blind beggar with the person who died ?
PS: Brother is not the answer.
The blind beggar was the sister of the person who died.
There is a dressing drawer which contains the following colored socks in pairs: Purple, Magenta, Crimson, White, Yellow and Turquoise. Now, the socks are paired and each pair is together in the matching set. There is no light in the room and you open the drawer and pick up a pair. Then, without noticing any color, you keep them back and pick up again.
Can you calculate the probability that the pair of socks was Yellow both the times?
Whenever two events are independent, we calculate the probability of both occurring as:
P(A and B) = P(A) * P(B)
P(Yellow) = 1/6
P(Yellow and Yellow) = P(Yellow) * P(Yellow)
= 1/6*1/6
= 1/36
You are camping with your friends. You have a flashlight for any emergency and have brought 8 batteries along with you. Your brother calls to tell you that four of those batteries are already dead.
Your flashlight requires two working batteries to run. What is the least number of pairs you will need to test to guarantee that you can get the flashlight on ?
7
You must first divide the batteries in three groups: a group of two batteries and two groups of three batteries each. Now you have made sure that one of the group has two working batteries.
Now both the groups with three batteries can form three possible combinations and the group with two batteries has just one combination.
3 + 3 + 1 = 7.
Before reading ahead, you must know the fact that only one of the person here is telling the truth.
A says that B is lying.
B says that C is lying.
C says both A and B are lying.
Can you find out who is speaking the truth?
B is speaking the truth.
A is lying when he says that B is lying. B is telling the truth when he says that C is lying. C is lying when he says that both A and B are lying since one of them is speaking the truth.
What does the following BrainBat signifies?
ABCDEFGHIJKLMNOPQRSTUVWYZ
QQQQQQQQQQQQQQQQQQQQQQQQQ.
No excuse.
It signifies that there is no X listed.
Suppose you drive to a picnic spot at 20 mph, then how fast you must go while returning back home on the same route such that your average speed becomes 40 mph?
infinite speed
Let us denote distance with d, time to get there by T, time to get back by t and the speed while travelling back with R.
Now by applying the simple time, distance and speed formula:
d = 20T
T = d/20
d = Rt
t = d/R
As you can see, we have the equations for both T and t now. We can now finally derive and equation for the round trip.
2d = 40(T + t)
2d = 40(d/20 + d/R)
2d = 40d(1/20 + 1/R)
1 = 20(R/20R + 20/20R)
20R = 20(R+20)
R = R + 20
You can clearly see that it is a paradox as to make the average speed 40 mph, you will have to travel back at an infinite speed. The faster you return, the quicker you can make it although your faster speed will offer a lesser impact on the average speed.
If you made the return trip instantly, it would be comparable to traveling double the distance in the same time that was taken on the one way trip.
Thus to reach the average speed of 40 mph, you must return with an infinite speed.