Substitute each of the capital letters in bold by a different base ten digit from 0 to 9 such that each of EEN, VIER and NEGEN is a perfect square. None of the numbers can contain any leading zero.

Disregarding the non leading zero condition, if we additionally impose the restriction that GIVEN is divisible by 23, then what will be the corresponding substitution?

solution aided by spreadsheet

1ST - NO LEADNG ZEROES

 EEN=441 NEGEN=14641  VIER= 3249

2nd stage:  een=004 negen=40804 , given=86204 vier=2601

1st-very easy ; 441 being an obvious choice
2nd- more tricky

edited to correct a minor typo

 

Edited on August 17, 2010, 6:46 pm

Posted by Ady TZIDON on 2010-08-17 12:36:55