Black or Cyan?

This blog post accounts for the highlights of the Australian IOI team’s fourth (and middle) day of training at the pre-departure camp at UNSW Sydney, as told by IOI team member Timmy Yao. Timmy is in Year 12, and representing Australia at the IOI for the first time this year.

Another day, another practice exam, and one day closer to IOI. And as the only remaining person who hasn’t written a blog post, I have the honour of doing so today.

Tonight’s game was based off of the first question of today’s exam — given a rectangular grid of squares coloured either black or cyan, find an arrangement using the least number of non-overlapping rectangles which covers all cyan squares and doesn’t cover any black squares.

BBBCCCCCCCCBBCBBCCCCCBBBB
BCCCCBBBBCCCCCCBBBBBCCBBB
CCCCCCCCCBBBBBBBBBCCCCCCC
CCCCBBCCCBBBBBBBBBCCCCCCC
BBBCCCCCCCCBBCBBCCCCCBBBB
CCBBBBBBCBCCCCCCCCCBBBCBC
BBBCBCCCCCCCBBBBCCCCCBBBB

Even under time pressure, we all found a solution using 21 rectangles, including Angus with his “very clear” drawing, pictured below:

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As this is the middle day of the pre-departure training camp, today had a free afternoon instead of our usual problem session. But before that, Josh took the time to explain the full solution to the above problem, though he called it “one of his most confusing explanations of a problem”, though the team has all seen at least one explanation where even Josh got himself confused). After that, Angus left us and visited his aunt while the rest of us returned to Perouse Lodge, where some of us worked on some problems, and others caught up with some schoolwork.