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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 870 · 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.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 79 (c) 80 (d) 70
  2. 2.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 141 (b) 150 (c) 142 (d) 132
  3. 3.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  4. 4.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 463 (c) 453 (d) 380
  5. 5.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 45 (c) 18 (d) 5
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 17 (b) 7 (c) 19 (d) 18
  7. 7.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 207 (c) 23 (d) 69
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 5 (b) 6 (c) 4 (d) 7
  9. 9.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 370 (c) 360 (d) 369
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 4 (d) 5
  11. 11.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 2 (b) 5 (c) 3 (d) 4
  13. 13.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 260 (c) 283 (d) 282
  14. 14.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 11 (d) 10
  15. 15.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) 21 (d) 63
  16. 16.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  17. 17.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
  18. 18.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 10 (c) 90 (d) 30
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 17 (b) 16 (c) 15 (d) 5
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 15 (b) 13 (c) 14 (d) 3
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 70? (a) 8 (b) 5 (c) 6 (d) 7
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
  23. 23.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 75 (b) 84 (c) 66 (d) 76
  24. 24.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 368 (b) 435 (c) 445 (d) 444
  25. 25.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 9 (b) 20 (c) 19 (d) 21
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 4 (b) 2 (c) 3 (d) 1
  28. 28.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 120 (c) 138 (d) 129
  29. 29.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) 45 (b) 48 (c) 135 (d) 15
  30. 30.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) 19 (b) 171 (c) 57 (d) 60
  31. 31.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 93 (b) 94 (c) 84 (d) 102
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 14 (b) 5 (c) 15 (d) 16
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 7 (b) 17 (c) 18 (d) 16
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 18 (b) 6 (c) 17 (d) 16
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 18 (b) 19 (c) 8 (d) 20
  36. 36.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  37. 37.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) 162 (b) 57 (c) 18 (d) 54
  38. 38.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 415 (c) 405 (d) 348
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 12 (b) 11 (c) 9 (d) 8
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 18 (b) 19 (c) 17 (d) 8

Answer key

  1. 79
  2. 141
  3. 8
  4. 462
  5. 15
  6. 18
  7. 69
  8. 6
  9. 369
  10. 4
  11. 6
  12. 4
  13. 282
  14. 9
  15. 21
  16. 3
  17. 4
  18. 30
  19. 16
  20. 14
  21. 7
  22. 2
  23. 75
  24. 444
  25. 6
  26. 20
  27. 3
  28. 129
  29. 45
  30. 57
  31. 93
  32. 15
  33. 17
  34. 17
  35. 19
  36. 4
  37. 54
  38. 414
  39. 11
  40. 18

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