Clock Teasers

Question 1:

Find the angle between the hands of a clock.

Question 2:

The hour and minute hands are at equal distance from the 6 hour, what time will it be exactly?

Question 3:

Find out how many times the minute hand and hour hand exactly match over a 12-hour cycle.How often the second hand and minute hand match each other exactly

  

Solution 1:

Minutes Angle = (360 * m) / 60 = 6m where m is the minutes.
Hour Angle = ((360 * h) / 12) + (360 * m / 12 * 60)
Hour Angle - Minutes Angle = 30h - 11m/2

Solution 2:

Say answer is "8 hour X minute". According as proposition, the angle between the minute hand and "mark 4" of the watch is equal to the angle between the hour hand and "mark 8" of the watch. 

We know in 60 minutes the minute hand makes 360 degrees (360/60=6 degrees per minute) and the hour hand makes 360/12=30 degrees (30/60=1/2 degrees per minute). 

Therefore, (20-X) minutes corresponds to 6(20-X) degrees (this is the angle between the minute hand and "mark 4"). 

And in X minutes the hour hand makes X/2 degrees with "mark 8". 

Thus, X/2=6(20-X) gives X=18 minutes 27 and 9/13 second. 

So, the answer is 8 hour, 18 minutes, 27 9/13 second.

Solution 3:

Between 12:00 and 1:00, the minute hand is always ahead of the hour hand. Then somewhere slightly past 5 minutes after 1:00, the hour and minute hands are in the exact same position. If you have a clock or watch on which you can manipulate the time, try this for yourself.

In this way, the minute hand will pass over the hour hand ten more times, once each hour between 1 and 2, 3 and 4, and so on, until the hour between 10 and 11. Between 11 and 12, the minute hand never catches up to the hour hand until exactly 12:00, when the hands line up again. The hands match up 12 times in a complete cycle, including both the starting and ending positions.

Measure 9 minutes

You are given two hourglasses. One measures 4 minutes and one measures 7 minutes. How would you measure exactly 9 minutes?

consecutive sum is perfect square

Arrange numbers from 1 to 16 such that the sum of every two consecutive numbers in the arrangement is a perfect square (you can use a number only once).

Weigh a plane

How would you weigh a plane without using scales ?

Jelly Beans

You have a bucket of jelly beans. Some are red, some are blue, and some green. With your eyes closed, pick out 2 of a like color. How many do you have to grab to be sure you have 2 of the same?

Find defective ball

You have 8 balls. One of them is defective and weighs less than others. You have a balance to measure balls against each other. In 2 weighings how do you find the defective one?

Level of water

If you are on a boat and you throw out a suitcase, will the level of water increase or decrease?

Place 3 identical coins

In how many ways 3 identical coins can be placed in 5x5 grid so that no two coin come in same row and same column

Round MAnhole Covers

Why are manhole covers round? Do manhole covers really need to be circular?

Unbiased decision from biased coin

You are given biased coin. Find unbiased decision out of it?

Concept:

When we have a biased coin, then the probability of a head and a tail is not the same. Let us say the probability of coming up with a head(H) is p, so the the probability of tail(T) would be 1-p. The dice would be biased when p > 0.5 or vice-verse.

The task at hand is to stimulate a condition where the probability of occurrence of two events is the same. That cannot be done with a single toss of the dice, so we need to think a little out of the box.

Throw the biased coin twice.

Classify it as true for HT and false for TH. Both of these occur with probability=p*(1-p), and hence unbiased.
Ignore the other 2 events namely HH and TT.

Probability of Parking Slot

The probability of finding the parking slot occupied is 1/3. You find it empty for 9 consecutive days. Find the probability that it will be empty on the 10th day.

Concept:
The answer to this question is 2/3, why ? Read the question carefully, it says what is the probability of finding it empty on the 10th day. Now in probability if an event has already happened it cannot have an effect on the probability of an event to occur in future. The parking slot has been empty for 9 days but that does not effect the 10th day.

Had the question been what is the probability of finding a parking slot empty for 10 consecutive days then the answer would have been (2/3)^10.