Enigma 1394: Squares and triangles
8 September 2013
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From New Scientist #2554, 3rd June 2006
Any number which is the sum of all the perfect squares from 1 to x² is called a square pyramidal number (such as 1, 5, 14, 30, 55). Any number which is the sum of the first x triangular numbers is called a tetrahedral number (such as 1, 4, 10, 20, 35). Within each of the following two statements digits have been consistently replaced by capital letters, different letters being used for different digits. But the two statements are entirely distinct – a letter need not have the same value in one statement as in the other.
Statement 1: ONE and FIVE are both odd square pyramidal numbers.
Statement 2: ONE is an odd tetrahedral number and FOUR is an even tetrahedral number.
Find the numbers represented by: (a) ONE and FIVE in Statement 1, and (b) ONE and FOUR in Statement 2.
This is the 500th Enigma puzzle published to the site. Hooray!
There is now complete coverage from June 2006 to the most recent puzzle (i.e. the last seven years), and also Classic puzzles from the start of Enigma in February 1979 up to August 1981. The most recent puzzle published is Enigma 1765, so this puts us at just over 28% of all Enigma puzzles ever published available on the site.