Question 25
In the equation below, $a,b,c$ are digits, $\overline{aa}$ and $\overline{bb}$ are two-digit numbers, and $\overline{cccc}$ is a four-digit number:
$$(\overline{aa})^2+\overline{bb}=\overline{cccc}.$$
What is the largest possible value of $a+b+c$?
The repeated digits denote place-value numerals, not products; $a,b,c$ are nonzero and need not be different.
Answer format: enter one whole number without units; leading zeros are optional. The source answer sheet uses four digits (for example, 7 is shaded as 0007).
$$(\overline{aa})^2+\overline{bb}=\overline{cccc}.$$
What is the largest possible value of $a+b+c$?
The repeated digits denote place-value numerals, not products; $a,b,c$ are nonzero and need not be different.
Answer format: enter one whole number without units; leading zeros are optional. The source answer sheet uses four digits (for example, 7 is shaded as 0007).