Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 4 · 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.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 520 (b) 418 (c) 519 (d) 510
2. 2.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1
3. 3.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) 7 (c) 21 (d) 24
4. 4.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) 27 (b) 24 (c) 8 (d) 72
5. 5.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 6 (d) 10
6. 6.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) 16 (b) 144 (c) 48 (d) 51
7. 7.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 57 (c) 162 (d) 18
8. 8.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 49 (b) 50 (c) 58 (d) 40
9. 9.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 470 (b) 588 (c) 598 (d) 597
10. 10.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 316 (c) 306 (d) 315
11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 14 (b) 15 (c) 16 (d) 4
12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 18 (b) 16 (c) 17 (d) 6
13. 13.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
14. 14.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 427 (c) 426 (d) 356
15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 7 (b) 17 (c) 19 (d) 18
16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 17 (b) 16 (c) 5 (d) 15
17. 17.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
18. 18.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 157 (c) 158 (d) 166
19. 19.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 228 (c) 225 (d) 235
20. 20.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 478 (c) 600 (d) 609
21. 21.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) 51 (c) 54 (d) 153
22. 22.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 549 (c) 558 (d) 559
23. 23.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 99 (c) 36 (d) 33
24. 24.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3
25. 25.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
26. 26.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 48 (c) 15 (d) 45
27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 16 (b) 7 (c) 18 (d) 17
28. 28.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 201 (c) 211 (d) 210
29. 29.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 2 (d) 4
30. 30.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 66 (c) 198 (d) 22
31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 17 (b) 16 (c) 7 (d) 18
32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 18 (b) 7 (c) 16 (d) 17
33. 33.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 71 (c) 72 (d) 62
34. 34.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 68 (c) 67 (d) 58
35. 35.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 537 (c) 547 (d) 546
36. 36.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 8 (b) 6 (c) 5 (d) 7
38. 38.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 636 (c) 496 (d) 637
39. 39.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 198 (c) 189 (d) 180
40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 9 (b) 19 (c) 20 (d) 21

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