Q1.
1. Find the missing numbers such that there is no remainder. Remember, there could be more than one solution. The ten puzzles are: 4)480(□□0 ; 3)906(□0□ ; 20)400(□0 ; 50)100□(□0 ; □)8□8(21□ ; 3)□36(3□□ ; □)88(□□ ; □)9□0(□□□ ; □)180(□□□ ; □)6,480(□□□
Answer
| Puzzle | Filled in | How to find it | Other answers |
|---|---|---|---|
| 4) 480 ( □ □ 0 | 4) 480 ( 1 2 0 | 480 ÷ 4 = 120 | only one |
| 3) 906 ( □ 0 □ | 3) 906 ( 3 0 2 | 906 ÷ 3 = 302 | only one |
| 20) 400 ( □ 0 | 20) 400 ( 2 0 | 400 ÷ 20 = 20 | only one |
| 50) 100 □ ( □ 0 | 50) 1000 ( 2 0 | 50 × 20 = 1000, so the missing digit is 0 | only one |
| □) 8 □ 8 ( 2 1 □ | 4) 848 ( 2 1 2 | 4 × 212 = 848 | 4) 868 ( 2 1 7 |
| 3) □ 3 6 ( 3 □ □ | 3) 936 ( 3 1 2 | 3 × 312 = 936 | only one |
| □) 8 8 ( □ □ | 4) 88 ( 2 2 | 4 × 22 = 88 | 2) 88 ( 4 4 and 8) 88 ( 1 1 |
| □) 9 □ 0 ( □ □ □ | 3) 900 ( 3 0 0 | 3 × 300 = 900 | 2) 900 ( 4 5 0, 5) 900 ( 1 8 0, 4) 920 ( 2 3 0 … |
| □) 1 8 0 ( □ □ □ | 1) 180 ( 1 8 0 | only a divisor of 1 keeps the quotient 3-digit | only one |
| □) 6,4 8 0 ( □ □ □ | 8) 6480 ( 8 1 0 | 8 × 810 = 6480 | 9) 6480 ( 7 2 0 |
How to attack a puzzle like this — the method.
- Count the boxes in the quotient. That tells you how many digits the answer must have.
- Use any digit already printed. In 3) □36 ( 3□□, the quotient starts with 3 and the dividend ends in 36. Since 3 × 3 hundreds = 9 hundreds, the dividend must start with 9.
- Multiply back to test. 3 × 312 = 936 ✓ — the printed digits all match, so it is right.
One shown in full — □) 8 □ 8 ( 2 1 □:
The quotient is between 210 and 219
The dividend starts with 8 and ends with 8
Try divisor 4: 4 × 212 = 848 ✓ (8 _ 8 with the middle digit 4)
Also 4 × 217 = 868 ✓ (8 _ 8 with the middle digit 6)
No other divisor works
The dividend starts with 8 and ends with 8
Try divisor 4: 4 × 212 = 848 ✓ (8 _ 8 with the middle digit 4)
Also 4 × 217 = 868 ✓ (8 _ 8 with the middle digit 6)
No other divisor works
About □) 180 ( □□□: the quotient must have 3 digits. 180 ÷ 2 = 90 has only 2 digits, and every larger divisor gives an even smaller answer. So the divisor has to be 1, giving 180 ÷ 1 = 180.