TTH:
and the # should be 144,837
Just too clever! :wink:
First of all get all the three digit squares where the first two numbers are the same. This produces 225 or 441, so the value of E is either 2 or 4, and N is either 5 or 1.
I get all 5 digit square numbers where the first number matched the last number, and the second number matched the fourth number. Only show the numbers where the first number, N, equalled 5 or 1, and the second number, E, equalled 2 or 4. Make sure that the third number, G, was not the same as any of the other numbers. This produced two possible answers, 12321 or 14641.
From this, we can see that if EEN is 225, there is no possible value for NEGEN. Therefore, EEN must be 441 and NEGEN must be 14641.
Then get all the possible values of four digit squares where the numbers were all unique and the 3rd number, E, was 4. This produced 5 possible answers, 1849, 3249, 5041, 6241, 8649.
From this, the only possible solution is 3249. All of the other answers contain numbers that have already been represented by a different letter previously.
So 441 x 3249 x 14641 = 20977756569.
The square root of this = 144837
Mark writes, "Answer" is full of "delight." I like it."
So that's what I was thinking!
PRBOPUERYTGY
GWETROUSDT
GO IT IT IT IT
