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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 253 · 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 two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 16 (b) 18 (c) 17 (d) 6
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 15 (b) 14 (c) 3 (d) 13
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 7 (b) 17 (c) 16 (d) 18
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 13 (b) 14 (c) 4 (d) 15
  6. 6.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 379 (c) 369 (d) 324
  7. 7.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 610 (c) 600 (d) 478
  8. 8.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 126 (c) 136 (d) 135
  9. 9.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  11. 11.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  12. 12.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 13 (c) 39 (d) 42
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
  14. 14.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 270 (c) 280 (d) 279
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 18 (b) 19 (c) 20 (d) 9
  16. 16.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) 30 (b) 27 (c) 9 (d) 81
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 5 (b) 13 (c) 12 (d) 14
  18. 18.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 471 (b) 386 (c) 472 (d) 462
  19. 19.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 4 (b) 5 (c) 2 (d) 3
  21. 21.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 46 (c) 36 (d) 45
  22. 22.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 131 (c) 122 (d) 140
  23. 23.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  24. 24.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 77 (b) 78 (c) 86 (d) 68
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 4 (b) 3 (c) 2 (d) 1
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 44? (a) 5 (b) 3 (c) 4 (d) 2
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 19 (b) 20 (c) 8 (d) 18
  28. 28.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 3 (b) 4 (c) 1 (d) 2
  30. 30.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 57 (b) 58 (c) 48 (d) 66
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 21 (b) 19 (c) 20 (d) 9
  32. 32.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  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) 7 (b) 24 (c) 63 (d) 21
  34. 34.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 330 (c) 387 (d) 388
  35. 35.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 198 (c) 204 (d) 199
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 2 (b) 5 (c) 3 (d) 4
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 4 (b) 3 (c) 2 (d) 1
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 18 (d) 9
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 17 (b) 7 (c) 19 (d) 18
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 18 (b) 20 (c) 19 (d) 8

Answer key

  1. 3
  2. 17
  3. 14
  4. 17
  5. 14
  6. 378
  7. 609
  8. 135
  9. 9
  10. 8
  11. 4
  12. 39
  13. 8
  14. 279
  15. 19
  16. 27
  17. 13
  18. 471
  19. 5
  20. 4
  21. 45
  22. 131
  23. 4
  24. 77
  25. 3
  26. 4
  27. 19
  28. 6
  29. 3
  30. 57
  31. 20
  32. 2
  33. 21
  34. 387
  35. 198
  36. 4
  37. 3
  38. 19
  39. 18
  40. 19

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