A medium question on number puzzles for P2–P4, with a step-by-step solution, diagrams and the answer. Number puzzles and made-up operations appear in the Hua Xia Cup from the P1 and P2 first rounds to the P6 finals.
The question
May copied out a subtraction but missed three digits, shown as □.
Each □ stands for one digit.
3
−28
653
What is the number on the top line?
Show the hints (2)
💡Hint 1: Turn the subtraction round and check it by adding: answer + number taken away = top number.
💡Hint 2: Start with the ones of 653 plus the second line: 3 + 8 gives the top number's ones digit. Keep track of every carry.
Worked solution
Have a go first, then read the solution step by step.
1.Turned round: 653 + the second line = the top line.
2.Ones: 3 + 8 = 11, so the top line ends in 1, carrying 1.
3.Tens: 5 + □ + 1 must end in 3, so the second line's □ is 7 (5 + 7 + 1 = 13, carrying 1).
4.Hundreds: 6 + 2 + 1 = 9, so the top line starts with 9.
5.The top line is 931. Check: 931 − 278 = 653.
⚠️Common mistake: forgetting a carry (a borrow, in the subtraction), which puts one □ out by 1.
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