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
Since ANN and IAN don't share a common factor, N isn't even or equal to 5. The constraint A<N<G<I<E means N can range from 2 to 6, so N=3.
Either ANN=133 and IAN one of 513,613,713,813 or ANN=233 and IAN one of 523,623,723,823.
I then multiplied each value of ANN by each value of IAN and by the number that made the result end in I and still be six digits.
The only solution found was ANN=233 and IAN=623, making ANGIE=23568, GEMINI=580636 and ENIGMA=836502.
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Posted by xdog
on 2024-09-20 18:03:57 |
solution
