Reconstruct from number clues

Find a two-digit number whose digits add to 9 and multiply to 18. Test factor pairs that are digits: 2 and 9 have the right product but the wrong sum. The pair 3 and 6 fits both clues. A positive product rules out zero.

The sum and product cannot distinguish 36 from 63. The third clue uses positions counted from the left: first digit × 1, second digit × 2, then add. The required total is 15.

For 36, 1 × 3 + 2 × 6 = 15. For 63, 1 × 6 + 2 × 3 = 12. So 36 fits all three clues. For longer numbers, continue with weights 3 and 4. Check every clue after arranging the digits.

Complete the square 1□4. Its leading 1 places it between 100 and 199, so test roots 10–14. Their squares are 100, 121, 144, 169 and 196. Only 144 matches the visible 1 and 4: 12² = 144. Enter 144, not 12 and not just the missing digit 4.

Complete the cube 1□31. Its leading 1 places it between 1000 and 1999. Since 10³ = 1000 and 13³ = 2197, check roots 10–12: their cubes are 1000, 1331 and 1728. Only 1331 fits every visible position. Verify 11 × 11 × 11 = 1331, then enter the whole number.

A new two-digit number has digit sum 6, digit product 8 and position-weighted total 10. The digits are 2 and 4. Compare both orders using first digit × 1 plus second digit × 2.

The next practice opens in English at Extended, Level 1. It includes digit constraints, missing square and cube digits, and one Classic question. Read the instructions for each question and enter the whole requested number.