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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 336 · 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 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 504 (c) 408 (d) 505
  2. 2.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 2 (d) 3
  3. 3.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 176 (c) 175 (d) 184
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 7 (d) 17
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 65? (a) 18 (b) 6 (c) 16 (d) 17
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 57? (a) 13 (b) 14 (c) 5 (d) 15
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 5 (b) 7 (c) 8 (d) 6
  8. 8.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) 19 (c) 171 (d) 57
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 17 (b) 18 (c) 8 (d) 19
  10. 10.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 4 (b) 3 (c) 2 (d) 5
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 18 (b) 7 (c) 17 (d) 19
  13. 13.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 537 (c) 538 (d) 528
  14. 14.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) 15 (b) 45 (c) 48 (d) 135
  15. 15.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 494 (b) 624 (c) 633 (d) 634
  16. 16.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 82 (c) 92 (d) 91
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
  18. 18.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
  19. 19.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
  20. 20.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 128 (c) 136 (d) 127
  21. 21.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 12 (d) 7
  22. 22.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) 54 (c) 153 (d) 51
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 3 (b) 5 (c) 2 (d) 4
  24. 24.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 170 (c) 188 (d) 179
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 4 (b) 16 (c) 14 (d) 15
  26. 26.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) 136 (c) 135 (d) 126
  27. 27.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 204 (c) 195 (d) 205
  28. 28.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) 582 (c) 592 (d) 466
  29. 29.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 168 (c) 186 (d) 177
  30. 30.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 589 (c) 464 (d) 588
  31. 31.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 171 (b) 180 (c) 172 (d) 162
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 9 (b) 21 (c) 19 (d) 20
  33. 33.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 526 (c) 516 (d) 422
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 7 (b) 11 (c) 14 (d) 13
  35. 35.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) 108 (b) 12 (c) 36 (d) 39
  36. 36.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 586 (b) 576 (c) 462 (d) 585
  37. 37.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 143 (b) 144 (c) 134 (d) 152
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 4 (b) 6 (c) 3 (d) 5
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 6 (b) 7 (c) 9 (d) 8
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 1 (b) 4 (c) 3 (d) 2

Answer key

  1. 504
  2. 2
  3. 175
  4. 18
  5. 17
  6. 14
  7. 7
  8. 57
  9. 18
  10. 4
  11. 4
  12. 18
  13. 537
  14. 45
  15. 633
  16. 91
  17. 3
  18. 5
  19. 18
  20. 127
  21. 8
  22. 51
  23. 4
  24. 179
  25. 15
  26. 135
  27. 204
  28. 591
  29. 177
  30. 588
  31. 171
  32. 20
  33. 525
  34. 13
  35. 36
  36. 585
  37. 143
  38. 5
  39. 8
  40. 3

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