Angle between Clock Hands

I don’t have any specific puzzle in this particular topic but I thought I can cover the bases so that any problem based on this concept can be answered.

There is a ready-made solution from Wikipedia which has formulas to figure the angle out,

Degree_H = (60H + M)/2

Degree_M = 6M

Angle = | Degree_H – Degree_M |

or

Angle = | (60H – 11M) / 2 |

eg: For Time 6:43,

Degree_H = (360+43) / 2 = 201.5

Degree_M = 6* 43 = 258

Angle = | 201.5 – 258 | = 56.5

The analytic method is simple for some times (Hours only like HH:MM = x:00 or times with perfect 60:min ratio like 6:15, 6:30)

Note: i) For every minute movement of the minute hand, the hour hand moves too. So angle between 6:30 is not 0 degrees.

ii) The problem is complicated if the minute mentioned is some odd number lik 6:11 or 6:43 and so on.

Personally, I just remember the formula and Note (i)

Rope around the Earth

Assume a rope is placed around the Earth (assume a absolutely spherical earth), with ends of the rope just meeting each other. Now, its length is increased by ‘x’ (so that the problem remains generic), but still the ends are just meeting. How far from the earth surface is the rope now?

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Ans: Initially, rope length L = circumference of the earth,

2*pi*r = L

After rope length is increased by ‘x’,

2*pi*(r+h) = L + x

To find out how far off the rope has been raised from the earth’s surface,

h = x / (2*pi)

Note: If the question is to find out how long the rope should be increased in order to raise it from the earth surface by ‘y’, then the answer would be 2*pi*y

Three Bags of Colored Balls

There are 3 closed bags containing  i) Blue balls only, ii) Red balls only and iii) Mixed balls. They are falsely named – i.e, bag named Blue is not blue, bag named Red is not red etc. How would you figure out which bag is which by opening just one bag?

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Ans:

Scenario 1: Open ‘Blue’. Since it is falsely named, it should be either red or mixed.

If it is red, then the bag ‘Red’  should contain mixed and the bag ‘Mixed’ should contain blue.

If it is mixed, then bag ‘Mixed’ should contain red and bag ‘Red’ should contain blue

Scenario 2: Open ‘Red’. Since it is falsely named, it should either contain blue or mixed.

If it is blue, then the bag ‘Blue’  should contain mixed and the bag ‘Mixed’ should contain red.

If it is mixed, then bag ‘Mixed’ should contain blue and bag ‘Blue’ should contain red

The Chessboard Conundrum

How many squares in a Chessboard?

A simple yet classic puzzle. If you look the problem from both ends, you can arrive at the answer faster. You start with 1 big 8×8 square and 4 7×7 square. The end is obviously 64 1×1 squares. By now, the pattern of sum of squares is clear to you.

No. of Squares = 1^2 + 2^2 + . . . + 8^2

=  204

Puzzles

Hi

A lot of interviews involve puzzles and brainteasers to evaluate the thought process of a candidate. So I thought it would be fun to include some puzzles in this blog. And, interview or not, puzzles are fun to solve. Hope you find them interesting.

Cheers

Ash