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IMSO 2025 Mathematics – International Essay Question 10

IMSO Maths · IMSO 2025 Mathematics – International Essay

Question 10

The diagram below shows a grid with 2 rows and 5 columns.

Question illustration

The grid must be completely covered using the following types of tiles namely:

- a 1-unit tile, which occupies one space $(1\times1)$ or
- a 2-unit tile, which occupies two spaces and may be placed either horizontally $(1\times2)$ or vertically $(2\times1)$.

Question illustration

How many different ways are there to completely cover the entire $2\times5$ grid without overlapping?