enigma1368.txt (c) 2006 by Charles Petzold
"Dutch Squares" by Richard England, New Scientist, 26 November 2005, page 52
EEN, VIER, and NEGEN (Dutch for 1, 4, and 9) are perfect squares with
numbers replacing letters. No number starts with zero. What's the
square root of EEN times VIER times NEGEN?
Only two perfect squares have three digits and begin with
double digits. They are 225 (15 squared) and 441 (21 squared).
If EEN is 225, then NEGEN is 52?25, but that doesn't work.
If EEN is 441, then NEGEN is 14641 (121 squared).
So VIER is ??4? but the question marks must be 2, 3, 5, 7, 8, or 9.
The only one that works is 3249 (57 squared).
The solution is 21 times 121 times 57 or 144,837.