TITLE: Perfect squares using 20 1's, 20 2's and 20 3's.
QUESTION [7 upvotes]: How many perfect squares can be formed using 20  1's, 20  2's and 20  3's. This is a recent exam question, which I had no clue how to solve?
There is some kind of trick here, since time allotted to solve it was just 4 minutes.

REPLY [3 votes]: \begin{array}{ll}
    20 *1 &= 20 \\
    20 *2 &= 40 \\
    20 *3 &= 60 \\
    ---------------
 \text{total} &= 120
 \end{array}

Now, Perfect square(s)...
$1+4+9+16+25+36+49 = 140$ ( I can remove $2$ number with total of $20$ ($4+16$))
that will lead to 
$1+9+25+36+49$ (i.e. $5$ numbers)
Answer: $5$ perfect squares can be formed..