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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 465 · 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.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) 21 (b) 54 (c) 18 (d) 6
  2. 2.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) 99 (b) 36 (c) 11 (d) 33
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 11 (b) 10 (c) 3 (d) 9
  4. 4.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
  5. 5.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 152 (c) 144 (d) 143
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 17 (b) 7 (c) 18 (d) 19
  7. 7.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) 60 (b) 57 (c) 19 (d) 171
  8. 8.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 288 (c) 297 (d) 298
  9. 9.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 592 (c) 466 (d) 582
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 14 (b) 16 (c) 4 (d) 15
  12. 12.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 113 (b) 104 (c) 122 (d) 114
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 1 (b) 4 (c) 2 (d) 3
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 60? (a) 17 (b) 16 (c) 15 (d) 6
  15. 15.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) 10 (b) 33 (c) 30 (d) 90
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 9 (d) 21
  17. 17.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 94? (a) 18 (b) 20 (c) 9 (d) 19
  19. 19.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 486 (c) 496 (d) 495
  20. 20.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 562 (c) 446 (d) 561
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 66? (a) 5 (b) 4 (c) 6 (d) 7
  22. 22.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 19 (b) 20 (c) 18 (d) 8
  24. 24.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) 18 (b) 5 (c) 45 (d) 15
  25. 25.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  26. 26.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
  27. 27.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 31 (b) 22 (c) 40 (d) 32
  28. 28.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) 13 (b) 39 (c) 42 (d) 117
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 4 (b) 2 (c) 3 (d) 5
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 66? (a) 14 (b) 6 (c) 13 (d) 15
  31. 31.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) 81 (b) 30 (c) 9 (d) 27
  32. 32.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  33. 33.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 260 (b) 273 (c) 282 (d) 283
  34. 34.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 50 (c) 49 (d) 58
  35. 35.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) 72 (b) 27 (c) 8 (d) 24
  36. 36.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 8 (b) 17 (c) 19 (d) 18
  38. 38.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 211 (c) 212 (d) 210
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 17 (b) 6 (c) 18 (d) 16
  40. 40.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8

Answer key

  1. 18
  2. 33
  3. 10
  4. 5
  5. 143
  6. 18
  7. 57
  8. 297
  9. 591
  10. 8
  11. 15
  12. 113
  13. 3
  14. 16
  15. 30
  16. 20
  17. 5
  18. 19
  19. 495
  20. 561
  21. 6
  22. 8
  23. 19
  24. 15
  25. 3
  26. 51
  27. 31
  28. 39
  29. 4
  30. 14
  31. 27
  32. 2
  33. 282
  34. 49
  35. 24
  36. 6
  37. 18
  38. 210
  39. 17
  40. 7

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