Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 952 · 40 questions

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

1. 1.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 189 (c) 21 (d) 63
2. 2.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 72 (c) 24 (d) 75
3. 3.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 36 (c) 12 (d) 108
4. 4.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 18 (b) 9 (c) 20 (d) 19
6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 3 (b) 4 (c) 2 (d) 5
7. 7.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 592 (c) 591 (d) 582
8. 8.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 439 (b) 429 (c) 364 (d) 438
9. 9.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
10. 10.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 54 (c) 153 (d) 51
11. 11.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 174 (c) 192 (d) 183
12. 12.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
13. 13.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 72 (c) 27 (d) 24
14. 14.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 50 (c) 41 (d) 42
15. 15.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 12 (b) 10 (c) 13 (d) 9
17. 17.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 7 (b) 4 (c) 5 (d) 6
19. 19.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 236 (b) 247 (c) 246 (d) 237
20. 20.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 133 (b) 124 (c) 142 (d) 134
21. 21.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 604 (c) 603 (d) 594
22. 22.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
23. 23.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 171 (c) 60 (d) 19
24. 24.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 6 (d) 7
25. 25.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 244 (c) 259 (d) 258
26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 17 (b) 19 (c) 18 (d) 8
27. 27.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 540 (c) 531 (d) 541
28. 28.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 21 (c) 6 (d) 54
29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 5 (b) 4 (c) 6 (d) 3
30. 30.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 48 (c) 16 (d) 51
31. 31.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 21 (c) 7 (d) 24
32. 32.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 390 (c) 477 (d) 478
33. 33.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 177 (c) 168 (d) 178
34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 96? (a) 21 (b) 20 (c) 19 (d) 9
35. 35.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 126 (c) 14 (d) 42
36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 18 (b) 19 (c) 17 (d) 7
37. 37.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 511 (c) 412 (d) 501
38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 7 (b) 5 (c) 6 (d) 8
39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 5 (b) 2 (c) 4 (d) 3
40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 16 (b) 7 (c) 18 (d) 17

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