Problem of the Day -- Clock Hands

Clock Hands

Write a program to find the minimum angle between two hands on a 24 hour clock. For instance, the angle at 6:00 is 90 degrees and the angle at 18:00 is also 90 degrees. At 6:17 the degree is ~~3.5~~ 7.75 and at 18:17 it's ~~176.5~~ 172.25 (hooray for supplementary angles).

For fun, program this one up in a language you've never used before. Here is a list of esoteric languages to help you decide. There are some truly interesting languages on that list. Feel free to use a "standard" language as well if there's one out there that you've been looking to learn.

Permalink: http://problemotd.com/problem/clock-hands/

Comments:

Moliugas - 10 years, 9 months ago
What type of clock is this? Shouldn't the angle at 6 be 180 degrees? Hour hand at 6 hour and minute hand at 12?

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Steve Mostovoy - 10 years, 9 months ago

I have a solution, however it gives 7.75 for 6:17 and 172.25 for 18:17. Is the question correct? I've double checked my math and it seems to be accurate for a 24 hour clock.

My solution in C#: float AngleBetweenHands(string time) { string[] split = time.Split(':');

    int hour = int.Parse(split[0]);
    int minute = int.Parse(split[1]);

    float hourPercentage = minute / 60f;
    float hourHandAngle = ((hour + hourPercentage) / 24f) * 360;

    float minuteHandAngle = hourPercentage * 360;

    float difference = Math.Abs(hourHandAngle - minuteHandAngle);
    if (difference > 180) {
        return 360 - difference;
    }
    return difference;
}

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Steve Mostovoy - 10 years, 9 months ago
My apologies, the first two lines weren't in the code block.
```
float AngleBetweenHands(string time) {
    string[] split = time.Split(':');
```
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Tim - 10 years, 9 months ago
Could someone please explain this to me?

For instance, the angle at 6:00 is 90 degrees and the angle at 18:00 is also 90 degrees.

Isn't this 180 degrees?

At 6:17 the degree is 3.5 and at 18:17 it's 176.5 (hooray for supplementary angles).

Why aren't these the same? Shouldn't they roughly be 90 degrees?

I don't understand!

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Tim - 10 years, 9 months ago
Oh I get it now. Duh. It's a clock which displays all 24 hours in 360 degrees. So instead of a normal clock which shows 12 hours, this one runs half as slow and shows all 24 hours. So noon (12:00) is at the 12hr clock's 6 o'clock position. 6am is at the 12hr clocks 3'oclock position, 6pm is at the 12hr clock's 9'oclock position.

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Tim - 10 years, 9 months ago

Same issue: 7.75 172.25

public double convertToDegrees(double hour, double minutes) {

    double degreesPerHour = 360/24;
    double degreesPerMinute = 360/60;
    double minutesAsHour = minutes/60;

    double additionalHourDegrees = minutesAsHour * degreesPerHour;

    double degrees = (((hour*degreesPerHour)+additionalHourDegrees) - (minutes*degreesPerMinute));

    if (degrees<0)
        degrees = degrees * -1;

    if (degrees > 180) { 
        degrees -= 180;
    }

    return degrees;
}

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Max Burstein - 10 years, 9 months ago

Yea my math must have been off when I was working on this. The math seems to check out for 7.75 and 172.25. Thanks for the submission!

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Tim - 10 years, 9 months ago
Thanks for setting these problems Max, they're good fun.

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Bruno A - 10 years, 9 months ago

@Moliugas it's a 24 hour clock (so the hours dial goes from 0/24 to 23, I'm guessing) I'm having a little problem - I think I have the code nailed down, but my angles for 6:17 and 18:17 are 7.75 and 172.75 respectively. Don't know what I'm doing wrong.

#!/usr/bin/env ruby

time = ARGV.first

begin
 hours, minutes = time.split(':')

 hours    = Integer(hours)
 minutes  = Integer(minutes)

rescue ArgumentError
  abort('please use proper times, like 6:17 or 18:17')
end

minutes_hand_deg  = minutes * 6
hours_hand_deg    = (hours + ( minutes / 60.0 ).to_f ) * 15

diff = (hours_hand_deg - minutes_hand_deg).abs

diff -= 180 if diff > 180

puts "angle is #{diff}"

Thanks for the challenge!

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Carlos - 10 years, 9 months ago
I have the same results, Curious! My method is pretty uch the same except i did in java first, i wonder if we are wrong or HE is wrong :P

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Max Burstein - 10 years, 9 months ago

It's definitely possible I was wrong. I'm doing the math now and what you both are saying seems correct. The minute hand moves 360/60 = 6 degrees per minutes and the hour had moves 360/24 = 15 degrees per hour. So 617-(615+17*15/60)=7.75. I'm curious where I came up with 3.5.

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dave - 10 years, 9 months ago
you can use modulo instead of diff-=180 if diff > 180

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SpaceRacer - 10 years, 9 months ago

short ruby solution (learning ruby)

# time is of format <0-23>:<0-59>
def min_angle(time)
    h, m = time[0..-4].to_i, time[-2..-1].to_i
    ((h*60+m)/4.0 - m*6).abs % 180
end

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Pearce Keesling - 10 years, 9 months ago

I kept forgetting that the hour hand moves in between hours haha. Great problems, keep it up.

#include <iostream>
#include <sstream>
#include <cmath>
using namespace std;
int main(int argc, char *argv[])
{
    string buff(argv[1]);
    string hour("");
    string min("");
    string *target = &hour;
    for(string::iterator it = buff.begin();it<buff.end();it++)
    {
        if(*it==':' || *it=='h')
        {
            it++;
            target = &min;
            }
            *target += *it;
    }
    float h,m;
    stringstream(hour) >> h;
    stringstream(min) >> m;
    float answer = fabs(((h+m/60)/24 - m/60) * 360);
    if(answer > 180) answer = 360 - answer;
    cout << answer << endl;
    return 0;
}

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Flavio - 10 years, 9 months ago

A C++ version not using pows and logs only plain integer operators:

using namespace std;

int main()
{
    long long l,m,r;

    for (;;) {
        cout << "0 to finish" << endl;
        cin >> r;
        if (!r) break;
        l=0;
        if (r > 9) do {
            l = l * 10 + r % 10;
            r /= 10;
        } while (l < r);
        cout << (l && l == r || r && l / 10 == r || !l ? "" : "not ") << "Palindromic" << endl;
    }
    return 0;
}

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Flavio - 10 years, 9 months ago
Weird placed solution for yesterday's problem here...

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Max Burstein - 10 years, 9 months ago

If you had the problem open on the home page before midnight and then posted it, it would go to whatever the current problem is. I just fixed this so it shouldn't happen again.

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Anonymous - 10 years, 9 months ago

Another one in J.

clockhands=: 3 : 0
  'h m'=. y
  mquot=. m % 60
  hquot=. (mquot % 24) + h % 24
  360&- ` ] @. (<&180) 360 * | hquot - mquot
)

echo clockhands 6 17   NB. => 7.75
echo clockhands 18 17  NB. => 172.25

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Anonymous - 10 years, 9 months ago
After reading the other solutions I see that we can make this a little more 'esoteric' ...
```
clockhands=: 3 : 0
  'h m'=. y
  360&- ` ] @. (<&180) | (6 * m) -~ 15 * (m % 60) + h
)
```
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Ethan - 10 years, 9 months ago
I don't get where the answers are coming from. 6:17 is 3.5 degrees? If you look at a 24 hour clock it should be around 30 degrees. I got 39.

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Anonymous - 10 years, 9 months ago
On a 24-h clock, the 6 is where the 3 is on a normal 12-h clock. East on a compass.

And 17 min is just a few degrees past that.

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tehmagik - 10 years, 9 months ago
Some simple python <code> def CalculateAngle(time): hour, minute = (float(x) for x in time.split(':')) angle = ((hour+minute/60)/24 - minute/60)*360 print('Angle for %s is: %.2f' % (time,abs(angle) if abs(angle) <= 180 else 360-abs(angle))) </code>

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anon - 10 years, 9 months ago

def CalculateAngle(time):
    hour, minute = (float(x) for x in time.split(':'))
    angle = ((hour+minute/60)/24 - minute/60)*360
    print('Angle for %s is: %.2f' % (time,abs(angle) if     abs(angle) <= 180 else 360-abs(angle)))

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John - 10 years, 9 months ago

Went with Javascript again... Wanted to mess with currying, so mine works on a 24 hour clock, as well as a 12 hour, or even a 2 hour with 77 minutes per hour.

function degreesBetweenHands(hourInterval,minuteInterval){
  return function(time){
    var timeArr = time.split(':');
    var hour = parseInt(timeArr[0]);
    var minute = parseInt(timeArr[1]);
    var hourDeg = degreesFromNumber(Number(hourInterval))(hour+minute/60);
    var minuteDeg = degreesFromNumber(Number(minuteInterval))(minute);
    var diff = Math.abs(hourDeg-minuteDeg);
    return Math.min(diff,360-diff);
  }
  function degreesFromNumber(num){
    var full = 360;
    var numNum = Number(num);
    return function(interval){
      var timeNum = Number(interval);
      return timeNum/numNum*full;
    }
  }
}

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John - 10 years, 9 months ago
usage:
```
degreesBetweenHands(24,60)('6:17');
```
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Chris - 10 years, 9 months ago
I'm so lost here, does the minute hand not rotate around the entire clock per hour? Or does it move in tiny increments within the current clock hour?

It's been a while since I did geometry so I must be missing something, why is everyone dividing minutes by 60? I got 5.72.

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Max Burstein - 10 years, 9 months ago

The minutes hand does indeed go around the clock every hour. Post your code and let's see if we can figure it out.

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Paprika - 10 years, 9 months ago
Here is a solution in Ruby: def angle(hour, minute) dph = 360.0/24 dpm = 360.0/60 deg = ((dph * hour + minute/60.0*dph) - dpm * minute) % 360 return deg > 180.0 ? 360.0 - deg : deg end

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Paprika - 10 years, 9 months ago
Woops, I can swear that I indented the code with four spaces!

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Problem of the Day A new programming or logic puzzle every Mon-Fri

Clock Hands

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Problem of the Day
A new programming or logic puzzle every Mon-Fri