## Program to determine when the hands of a clock meet and align.

Write a program to determine all times of a day when the hands of a clock meet, i.e., are perfectly aligned at an angle of zero degrees.

**Step 1: ** First create a function that takes hours and minutes, and tells a true or false value whether the hands meet at that moment of time.

bool areAligned(int h, float m) { // first calculate angle for hours clock // The angle is measured in degrees // from the mark of number 12 clockwise. // so far how many minutes have elapsed? float totalMinutes = 60 * h + m; // hours clock travels (360 / 12 ) / 60 = // 0.5 degrees in one minute. so total degrees? float angleHours = totalMinutes * 0.5f; // next take the minutes hand // it travels 360 degrees in 60 minutes // so in one minute it travels = // 360 / 60 = 6 degrees. total angle? float angleMinutes = m * 6.0f; // the difference float angle = angleMinutes - angleHours; // if it is negative, make absolute if(angle < 0) { angle *= -1; } return angle < 0.1f; }

**Step 2: **Call the above function from your main. We will have to loop for all the moments of the day and check each point.

int main() { for(int h = 0; h < 12; h++) { for(int m = 0; m < 59; m++) { // check for each fractional second // at this minute for(int inc = 0; inc < 100; inc++) { float minute = m + (float)(inc/100.0); if(areAligned(h, minute)) { cout << "Aligned at: " << h; cout << ":" << minute; cout << endl; break; } } } } return 0; }

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This Blog Post/Article "Program to determine when the hands of a clock align" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2017-05-17.