Q1.
Fill the digits 1, 3, and 7 in ⬜⬜ × ⬜ to make the largest product possible.
Answer
Here p = 1, q = 3, r = 7. The rule gives multiplier 7 and multiplicand 31.
Largest = qp × r = 31 × 7 = 217
| Arrangement | Product | Arrangement | Product |
|---|---|---|---|
| 13 × 7 | 91 | 37 × 1 | 37 |
| 17 × 3 | 51 | 71 × 3 | 213 |
| 31 × 7 | 217 | 73 × 1 | 73 |
Tip: 71 × 3 = 213 comes close, and it is the arrangement that tempts most people — the biggest digit in the tens place looks right. But 31 × 7 = 10 × 3 × 7 + 1 × 7 = 210 + 7, while 71 × 3 = 10 × 7 × 3 + 1 × 3 = 210 + 3. Same first term; the second decides it.