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February 17th, 2018, 06:01 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 332 Thanks: 1  How to solve this problem regarding clock strikes?
Question: A clock strikes once at 1:00 Clock and twice at 2:00 clock, thrice at 3:00 clock, and so on, respectively. How many total strikes per day? Solution: 1 + 2 + 3 + 4.........+ 12 = 12(13)/2 = 78 × 2 = 156 (Answer) My doubt  how can a clock hits "once at 1:00 clock" if 1:00 clock happens twice per day, i.e. 1 am and 1 pm? Last edited by skipjack; February 17th, 2018 at 06:52 PM. 
February 17th, 2018, 06:12 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond 
When the clock shows one it strikes once, be it am or pm.

February 18th, 2018, 01:11 AM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 332 Thanks: 1  I think you misunderstood the question, In my question there is also a sentence which says " twice at 2:00 clock, thrice at 3:00 clock". if you say "When the clock shows one it strikes once, be it am or pm." then it is impossible to twice at 2:00 clock, thrice at 3:00 clock. Are you saying question is wrong? 
February 18th, 2018, 01:44 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond  At one pm the clock strikes once. At one am the clock strikes once. A two pm the clock strikes twice. At two am the clock strikes twice. At three pm the clock strikes thrice. At three am the clock strikes thrice. And so on.

February 18th, 2018, 02:08 AM  #5 
Senior Member Joined: Aug 2014 From: India Posts: 332 Thanks: 1  
February 18th, 2018, 02:10 AM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond 
The clock chimes twice! Google "definition of chime" if you don't know what that means.
Last edited by greg1313; February 18th, 2018 at 02:14 AM. 
February 18th, 2018, 02:29 AM  #7 
Senior Member Joined: Aug 2014 From: India Posts: 332 Thanks: 1 
Solution: 1 + 2 + 3 + 4.........+ 12 = 12(13)/2 = 78 × 2 = 156 (Answer) Why they multiple with 13 and divided with 2. Last edited by Ganesh Ujwal; February 18th, 2018 at 02:42 AM. 
February 18th, 2018, 02:56 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 19,725 Thanks: 1807 
The average of the first and last term is (1 + 12)/2 = 13/2. The sum is 12 (the number of terms) multiplied by the above average. 
February 18th, 2018, 03:05 AM  #9 
Senior Member Joined: Aug 2014 From: India Posts: 332 Thanks: 1  
February 18th, 2018, 04:14 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,320 Thanks: 936  

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