Question 1198924
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There are algebraic techniques that you could use to solve the problem, or to work parts of the problem.  But the conditions of the problem allow only a very few possible solutions, so trying each of them to find the answer is as good a method as any.<br>
The conditions of the problem say that the number PP is a 2-digit integer with both digits the same, an PQ is the next larger integer.  Try each possibility:<br>
11^2+12^2 -- don't even need to do the actual calculations; the sum is not 4 digits
22^2+23^2 = 484+529 = 1013
33^2+34^2 = 1089+1136 = 2225
44^2+45^2 = 1936+2025 = 3961
55^2+56^2 = 3025+3136 = 6161<br>
There is our answer. P = 5; Q = 6; R = 1<br>
ANSWER: P+Q+R = 12<br>