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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 211 · 40 questions
TalentJR

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.

NameDateTime takenScore ___ / 40
  1. 1.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 7 (b) 17 (c) 18 (d) 19
  2. 2.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
  4. 4.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  5. 5.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 478 (c) 468 (d) 477
  6. 6.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 579 (c) 580 (d) 570
  7. 7.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) 8 (c) 24 (d) 72
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 4 (b) 3 (c) 6 (d) 5
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 11 (b) 13 (c) 14 (d) 8
  10. 10.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 8 (d) 13
  11. 11.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 146 (c) 154 (d) 145
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 1 (b) 2 (c) 3 (d) 4
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 2 (b) 3 (c) 4 (d) 5
  14. 14.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) 12 (b) 36 (c) 108 (d) 39
  15. 15.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 306 (c) 282 (d) 315
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 19 (b) 20 (c) 21 (d) 9
  17. 17.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 460 (c) 459 (d) 378
  18. 18.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  19. 19.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  20. 20.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) 198 (b) 69 (c) 66 (d) 22
  21. 21.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) 24 (b) 72 (c) 75 (d) 216
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 16 (b) 18 (c) 6 (d) 17
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 81? (a) 17 (b) 18 (c) 8 (d) 19
  24. 24.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 81 (c) 90 (d) 82
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 21 (b) 19 (c) 20 (d) 9
  26. 26.The numbers 5 to 13 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) 30 (c) 81 (d) 9
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 10 (b) 7 (c) 6 (d) 9
  29. 29.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 97 (c) 88 (d) 98
  30. 30.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  31. 31.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 643 (b) 642 (c) 500 (d) 633
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 19 (b) 20 (c) 18 (d) 8
  33. 33.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) 24 (b) 7 (c) 63 (d) 21
  34. 34.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  35. 35.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 60 (c) 63 (d) 20
  36. 36.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 622 (b) 486 (c) 621 (d) 612
  37. 37.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
  38. 38.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 435 (c) 362 (d) 426
  39. 39.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  40. 40.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 328 (c) 290 (d) 327

Answer key

  1. 18
  2. 2
  3. 6
  4. 5
  5. 477
  6. 579
  7. 24
  8. 5
  9. 13
  10. 7
  11. 145
  12. 3
  13. 4
  14. 36
  15. 315
  16. 20
  17. 459
  18. 8
  19. 6
  20. 66
  21. 72
  22. 17
  23. 18
  24. 81
  25. 20
  26. 27
  27. 9
  28. 9
  29. 97
  30. 4
  31. 642
  32. 19
  33. 21
  34. 9
  35. 60
  36. 621
  37. 48
  38. 435
  39. 3
  40. 327

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