Enigma 1672: Heptagony
30 November 2011
Posted by on
From New Scientist #2838, 12th November 2011 [link]
I was surfing the internet recently, and found a reference to polygonal numbers. These are series such as the triangular numbers, pentagonal numbers and others, including the series of heptagonal numbers, which starts 1, 7, 18, 34… I asked my nephew to tell me the next member of this series, which he said was 55. Later he told me that he had found a set of six consecutive heptagonal numbers, all less than two million, where the difference between the first and last was divisible by all of the digits 1 to 9. One of the intermediate heptagonal numbers in this set was divisible by just four of these digits.
What was this heptagonal number?
Note: As originally published this Enigma asked for a set of five consecutive heptagonal numbers, which admits no solution. The magazine later issued this corrected puzzle.