An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Choose any three by three square of dates on a calendar page...
Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP
have equal areas. Prove X and Y divide the sides of PQRS in the
It is clear that each of a, b and c must be less than or equal to $10$. A brief inspection will show that the only combination of different square numbers which total $121$ is $81, 36, 4$, so the $a, b$ and $c$ are $2, 6$ and $9$.
This problem is taken from the UKMT Mathematical Challenges.View the archive of all weekly problems grouped by curriculum topic