MATH *IMPORTANT

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!!

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  1. 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

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  2. 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 ;)

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