HOW MANY SETS (A,B,C) OF THREE DIFFERENT,POSITIVE SINGLE DIGIT INTEGERS HAVE THE PROPERTY THAT A SQUARED + B SQUARED + C SQUARED IS A PERFECT SQUARE? please help me with this one a soon as possible its very important and i don't even know where to start!!

Question

Reiny · Answer

make 3 columns

A -- B ---C
try
1 1 1---- 1^2 + 1^2 + 1^2 = 3
have a list of perfect squares handy :
1 4 9 16 25 ... 225

is 3 in the list? NO
1 1 2 --- 6 , is 6 in the list ? NO
1 1 3 --- 11 , is 11 in the list ? NO
...
1 1 9 ---83, is 83 in the list ? NO

1 2 1 ---- already done
1 2 2 --- 9, is 9 in the list ? YEAHHHH
1 2 3 ---- 14 NO
1 2 4 --- 21 NO
etc

rather tedious, but do you get the idea?
there are many duplications
e.g. 4 3 2 came up in 2 3 4

DEREK · Answer

well i get that but i just don't c what the answer is becuase it takes forever to do this problem u have to use numbers ubtil you have them all. i am in mathcounts and it is totally competition i cant be up doing a problem like that isnt there a possible way to do it faster and this time maybe state the answer so i can work it backwards ;)