Logical Puzzles

Palm Tree

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.

No excuse.
It signifies that there is no X listed.

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.

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.

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

The blind beggar was the sister of the person who died.

Many of you might have tried making five different squares but that was not asked in the question. See the figure for the explanation.

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.

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.