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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 752 · 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 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 246 (c) 247 (d) 236
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 76? (a) 7 (b) 18 (c) 19 (d) 17
  3. 3.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 9 (d) 10
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 16 (b) 18 (c) 6 (d) 17
  5. 5.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 39 (b) 40 (c) 30 (d) 48
  6. 6.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 40 (c) 49 (d) 50
  7. 7.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) 72 (b) 216 (c) 24 (d) 75
  8. 8.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 493 (c) 483 (d) 400
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 17 (b) 18 (c) 19 (d) 8
  10. 10.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) 51 (b) 144 (c) 16 (d) 48
  11. 11.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) 33 (b) 99 (c) 36 (d) 11
  12. 12.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) 18 (b) 57 (c) 54 (d) 162
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 3 (b) 4 (c) 5 (d) 6
  14. 14.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) 18 (b) 21 (c) 6 (d) 54
  15. 15.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) 140 (c) 122 (d) 131
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 19 (d) 20
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 19 (b) 21 (c) 20 (d) 9
  18. 18.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) 39 (b) 42 (c) 13 (d) 117
  19. 19.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  20. 20.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
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 18 (d) 17
  22. 22.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 124 (c) 132 (d) 123
  23. 23.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  24. 24.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  25. 25.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) 171 (c) 19 (d) 57
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 72? (a) 6 (b) 8 (c) 5 (d) 7
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 63? (a) 6 (b) 10 (c) 11 (d) 8
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 7 (b) 16 (c) 18 (d) 17
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 9 (b) 20 (c) 21 (d) 19
  30. 30.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 137 (b) 128 (c) 138 (d) 146
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 5 (b) 17 (c) 15 (d) 16
  33. 33.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 598 (b) 470 (c) 588 (d) 597
  34. 34.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 213 (b) 223 (c) 222 (d) 220
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 4 (b) 6 (c) 5 (d) 3
  36. 36.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) 48 (b) 15 (c) 135 (d) 45
  37. 37.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  38. 38.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 465 (c) 388 (d) 475
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 18 (b) 19 (c) 7 (d) 17
  40. 40.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 153 (b) 162 (c) 144 (d) 154

Answer key

  1. 246
  2. 18
  3. 9
  4. 17
  5. 39
  6. 49
  7. 72
  8. 492
  9. 18
  10. 48
  11. 33
  12. 54
  13. 5
  14. 18
  15. 131
  16. 20
  17. 20
  18. 39
  19. 3
  20. 21
  21. 18
  22. 123
  23. 7
  24. 5
  25. 57
  26. 7
  27. 10
  28. 17
  29. 20
  30. 137
  31. 2
  32. 16
  33. 597
  34. 222
  35. 5
  36. 45
  37. 8
  38. 474
  39. 18
  40. 153

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