VTMO 2026 - Grade 8 - Semifinal - SET 07 - Self-study Question 9

A car travels at $55$ km/h. Its odometer initially reads the three-digit number $\overline{abc}$ and after a positive integer number of hours reads $\overline{cba}$. Given $a+b+c\le7$, find $a^2+b^2+c^2$.