1. The problem involves finding missing numbers in a set of rectangular boxes where arrows indicate multiplication or division relationships between the center number and the numbers on the sides. 2. Each box has a center number and four numbers around it connected by arrows. The arrows represent multiplication or division such that the side numbers are factors or multiples of the center number. 3. To solve for missing numbers, use the relationships: - If an arrow points from a side number to the center, the center number is a multiple of the side number. - If an arrow points from the center to a side number, the side number is a factor of the center number. 4. For each box, use the known numbers and the direction of arrows to set up equations and solve for the unknowns. 5. Example: For the box with center 12, and side numbers 6 and 4 with arrows 6 → 12 ← 4, since arrows point from 6 and 4 to 12, 12 is a multiple of both 6 and 4. This is consistent since 12 = 6 × 2 and 12 = 4 × 3. 6. Applying this logic to the box with center 12 and unknowns on the right and bottom sides: - The right side number has an arrow from center to side, so it divides 12. - The bottom side number has an arrow from side to center, so 12 is a multiple of it. 7. Using the other boxes similarly, solve for all missing numbers: - For the box with center 36 and unknowns on top and right sides: - Top side arrow points from side to center, so 36 is a multiple of the top side number. - Right side arrow points from center to side, so the side number divides 36. - For the box with center 63 and unknowns on top and left sides: - Top side arrow points from side to center, so 63 is a multiple of the top side number. - Left side arrow points from side to center, so 63 is a multiple of the left side number. - For the box with center 144 and unknown on the top side: - Top side arrow points from side to center, so 144 is a multiple of the top side number. - For the box with center 48 and unknown on the right and bottom sides: - Right side arrow points from center to side, so the side number divides 48. - Bottom side arrow points from side to center, so 48 is a multiple of the bottom side number. 8. Calculations: - Box with center 12: - Right side divides 12 and bottom side is a factor of 12. - Possible divisors of 12: 1, 2, 3, 4, 6, 12. - Given bottom side arrow points from side to center, bottom side could be 3 (since 12 = 3 × 4). - Right side arrow points from center to side, so right side divides 12, possible 2 or 3. - Since bottom side is 3, right side is 2. - Box with center 36: - Top side arrow points from side to center, so top side divides 36. - Right side arrow points from center to side, so right side divides 36. - Given left side is 3 and bottom side is 6. - Top side could be 6 (since 36 = 6 × 6). - Right side could be 6 (since 36 ÷ 6 = 6). - Box with center 63: - Top side arrow points from side to center, so top side divides 63. - Left side arrow points from side to center, so left side divides 63. - Given right side is 9 and bottom side is 49. - Top side could be 9 (since 63 = 9 × 7). - Left side could be 7 (since 63 = 7 × 9). - Box with center 144: - Top side arrow points from side to center, so top side divides 144. - Given left side is 12 and bottom side is 1. - Top side could be 12 (since 144 = 12 × 12). - Box with center 48: - Right side arrow points from center to side, so right side divides 48. - Bottom side arrow points from side to center, so bottom side divides 48. - Given left side is 4 and top side is 12. - Right side could be 8 (since 48 ÷ 6 = 8). - Bottom side could be 16 (since 48 = 16 × 3). Final answers for missing numbers: - Box with center 12: right side = 2, bottom side = 3 - Box with center 36: top side = 6, right side = 6 - Box with center 63: top side = 9, left side = 7 - Box with center 144: top side = 12 - Box with center 48: right side = 8, bottom side = 16