CEMC Euclid, 2008

Algebra Difficulty 2.0 Junior Prove it Canada

A $3 \times 3$ square frame is placed on a grid of numbers, as shown. In the example, the sum of the numbers inside the square frame is $108$ , and the middle number is $12$ . When the square frame is moved to a new position, the sum of its numbers becomes $279$ . In the frame's new position, what is the middle number?

Figure for this problem

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.