Gwyn's niece, Angela, has two younger twin siblings, Ann and Ian. To celebrate the twins’ birthday, she asked Gwyn to compose a puzzle in which their names feature. Here it is:

With different letters denoting different digits consistently throughout, and with no leading zeros appearing, the number denoted by GEMINI is exactly divisible by the numbers corresponding to ANN and IAN. These two three-digit numbers have no common factor. The number denoted by ANGIE has digits which increase from left to right.

What number corresponds to ENIGMA?

Note: Adapted from Enigma Number 1681 by Gwyn Owen which appeared in New Scientist on 18 January, 2012

ANN=233 IAN=623 ANGIE=23568

GEMINI=580636 ENIGMA=836502

I used a brute force code.

Note, ANN is prime and IAN is not.

Also, there are 9*8*7*6=3024 possibilities for 

ANGIE, given the constraints.

Beyond that, I wonder how the "analytic" solution 

would go....

Edited on September 19, 2024, 11:27 pm

Posted by Steven Lord on 2024-09-19 20:27:39