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IMAS 2024–2025 Junior Division First Round Question 19

IMAS · IMAS 2024–2025 Junior Division First Round

Question 19

Some shaded squares are located around a square grid and must be filled with one arrow each, drawn in a way that the arrow points vertically ($\uparrow$ and $\downarrow$), horizontally ($\rightarrow$ and $\leftarrow$) or diagonally ($\searrow$, $\swarrow$, $\nwarrow$ and $\nearrow$) along the grid. Each arrow must point to at least one unshaded square. The number of arrows pointing to each unshaded square in the grid equals the number shown in that square. The following diagram shows one example:

Question illustration

Ben has to completely fill in the arrows in the grid below, where some arrows were already pre-filled. After completing the task, what is the total number of $\nwarrow$ and $\searrow$ arrows that Ben used?

Question illustration
  1. 6
  2. 7
  3. 8
  4. 9
  5. 10