Enigma 1775: Third symphony
13 November 2013
Posted by on
From New Scientist #2943, 16th November 2013 [link]
I have in mind three numbers. Each is a multiple of 3 and consists of three different non-zero digits, just one of which is 3. For each of these numbers individually, three of the following six statements are true and three are false.
1) It is the product of three different numbers, each a prime.
2) It is a triangular number, that is of the series 1, 3, 6, 10, 15 …
3) It is a cube, or a cube plus 3.
4) It may be written as a single-digit prime followed by a two-digit prime.
5) The 3 is the first or last digit.
6) It may be written as a two-digit prime followed by a single-digit prime.
What are my three numbers?