An analog clock is a device that shows the time of day by moving two
pointers, an *hour hand* and a *minute hand*, through a
circle.
The hour hand moves uniformly clockwise through the circle once every
twelve hours.
The minute hand moves uniformly clockwise through the circle once every
hour.
The numbers 1 through 12 are arranged around the circumference of the
circle such that 12 is at the top, and each number *k* is
20° counterclockwise from the *k*+1.
At 12:00 midnight, both hands point directly to the 12.
At 12:30 AM, the hour hand points midway between the 12 and the 1, and
the minute hand points directly at the 6.
At 1:00 AM, the hour hand points directly to the 1 and the minute hand
points directly to the 12, and so forth.

Write a program to determine the angle between the hands of the clock at a specified time. Use any convenient angular measure.

At what times of day, to the nearest second, do the hands of the clock point in exactly opposite directions?

At what times of day, to the nearest second, do the hands of the clock make a right angle?

A *second hand* is a third pointer that moves uniformly
clockwise through the circle once every minute.
At 12:00 midnight, all three hands point directly to the 12.
Determine how many times per day all three hands of the clock are
collinear (either all three pointing exactly in the same direction, or
one pointing exactly opposite the other two).
Determine how many times per day the hands form one or two right angles
(either two pointing exactly in the same direction with the third at a
right angle, or two pointing exactly in opposite directions with the
third at a right angle).

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Copyright © 2002 Brian Hetrick

Page last updated 3 March 2002.

Tutorial

Building Blocks I

Control Flow II

Basic I/O

Algorithms

A First Program

Exercises

Clock Hands

Answers

Modularization

Data Structures I

Recursion

Program Attributes

Building Blocks II

Algorithm Analysis

Structuring

Data Structures II

Abstract Types

Objects

Problem Analysis

Reference Card