Maths Olympiad Prep

Library / CEMC Galois /33 of 97

CEMC Galois, 2004

Combinatorics Difficulty 2.0 Junior Prove it Canada

In “The Sun Game”, two players take turns placing discs numbered 1 to 9 in the circles on the board. Each number may only be used once. The object of the game is to be the first to place a disc so that the sum of the 3 numbers along a line through the centre circle is 15. If Avril places a 5 in the centre circle and then Bob places a 3, explain how Avril can win on her next turn.

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.