A Curious Clock Puzzle

fantastic-forest-clock.jpg

Draw two straight lines across the face of the clock in such a way so that the sum of the numbers in every section are the same. 

Solution 

The sum of all the hour numbers on the clock is 78. As the two lines would divide the clock face into three sections, the sum of the numbers in each section has to be 26. The rest is trial and error.

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My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. You can find me on Twitter` and Facebook. My email is edmarklaw@learnfunfacts.com

22 thoughts on “A Curious Clock Puzzle

  1. Since 78 is also divisible by two, you can draw five lines across the face, dividing it into six sections in which the sums of the numbers in each section are the same. A tip of the hat to Gauss.

    Liked by 1 person

    1. This has been known during the time of the Pythagoreans.

      That anecdote of Gauss is most likely apocryphal as many of these several accounts are have many differences and there is an absence of original source. The earliest sources that I have found are from German periodicals dated 1855, the year of Gauss’ death. Along with it, there were also several anecdotes of Gauss, but it seems that this is the only few ones that survived the test of time. Since then, it had been translated, modified and republished in several publications.

      Nonetheless, there is no doubt that Gauss could have thought of it. In fact, I myself who’s even not that good at math have intuitively come up with it (not similar with Gauss’ though as I did directly come up with the formula for triangular numbers based on the observation that 1 + 2 + 3 = 6; 3(4)/2) = 6, and so on. I have heard from Benjamin Arthur (a lightning calculator) that he came up with it (similar to the one by Gauss) when he was in second grade. Of course, he was ecstatic at the time. He was very disappointed though when he later learned that it was already known for more than 2000 years…

      Liked by 1 person

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