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

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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