Problem 23 · 2014 Math Kangaroo
Stretch
Spatial & Visual Reasoning
grid-countingcasework
In the figure on the right a few of the small squares will be painted grey. While doing this, no 2×2 block made of four small grey squares is allowed to appear. At most how many of the squares in the figure can be painted grey?
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Answer: D — 21
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Hint 1 of 3
The rule is broken the moment four grey squares make a full 2×2 block, so every 2×2 block needs at least one white square.
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Hint 2 of 3
To colour the MOST squares grey, leave as few white squares as you can while still breaking every 2×2 block.
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Hint 3 of 3
Spread your white squares out cleverly so each one spoils several 2×2 blocks at once.
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Approach: leave the fewest white squares that still break every 2x2 block
- Every little 2×2 group of squares must have at least one square left white, or it would be a forbidden block.
- To keep the most grey, place the white squares far apart so each white square breaks as many 2×2 blocks as possible.
- Doing this for the whole figure leaves just a few white squares, and the rest, 21 of them, can be grey.
- Answer: 21.
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