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AMO 2017 Grade 2 Question 15

AMO · AMO 2017 Grade 2

Question 15

There are 84 unit cubes arranged in 4 square layers with no space between the cubes as shown. The layers are 1 by 1, 3 by 3, 5 by 5, and 7 by 7. How many unit cubes are completely surrounded by six other unit cubes?

Question illustration