**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?

[enigma1775]

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This puzzle highlighted an inconsistency in the return values (now fixed) of the

is_triangular()function from theenigma.pylibrary. This Python program uses the latest version of that function, and runs in 36ms.Solution:The three numbers are 231, 273 and 435.I found the predicate ‘exactly’ was useful to check that a given number of items in a list are true.

I also set the configuration to multiple outputs to give the three (and only three) numbers fulfilling

the puzzle conditions