Q1.
Fill the yellow boxes with 1-digit numbers (multiplicands and multipliers) such that you get the products given in the white boxes. Fill the remaining white boxes with appropriate products.
Answer
The matrix as printed. The yellow boxes are empty; four products are already given.
The same matrix after filling it. The four given products are in black.
| × | ||||
|---|---|---|---|---|
| 32 | ||||
| 42 | ||||
| 45 | ||||
| 21 |
Start with the column that already has two products in it — 42 and 21.
21 = 3 × 7
42 = 6 × 7
The number common to both is 7.
So that yellow column box is 7. Its two row boxes are 6 and 3.
42 = 6 × 7
The number common to both is 7.
So that yellow column box is 7. Its two row boxes are 6 and 3.
Now the single products:
32 = 8 × 4 → row box 8, column box 4
45 = 9 × 5 → row box 9, column box 5
The last column has no product given, so any 1-digit number fits. We take 2.
45 = 9 × 5 → row box 9, column box 5
The last column has no product given, so any 1-digit number fits. We take 2.
Filling every white box gives:
| × | 4 | 5 | 7 | 2 |
|---|---|---|---|---|
| 8 | 32 | 40 | 56 | 16 |
| 6 | 24 | 30 | 42 | 12 |
| 9 | 36 | 45 | 63 | 18 |
| 3 | 12 | 15 | 21 | 6 |
Why it happens: A column box must divide every product printed in that column. Only 7 divides both 21 and 42, so 7 is forced.
Tip: Your answer may look different in the last column, and that is fine. Check that 32, 42, 45 and 21 still sit in their own places.