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AMO 2017 Secondary 3 (Grade 9) Question 18

AMO · AMO 2017 Secondary 3 (Grade 9)

Question 18

Jethro tiles a $10\text{ cm}\times15\text{ cm}$ floor with the pictured J-shaped tiles. Each tile consists of six $1\text{ cm}\times1\text{ cm}$ squares. Tiles may be turned, but may not be cut or overlap. What is the smallest uncovered area, in $\text{cm}^2$?

Interpretation: tiles follow the unit-square grid, as in the source construction.

Question illustration