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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 182 · 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 times is the digit 6 written when you write all the numbers from 1 to 90? (a) 18 (b) 9 (c) 20 (d) 19
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 6 (b) 4 (c) 3 (d) 5
  4. 4.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 262 (c) 246 (d) 252
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 7 (b) 9 (c) 10 (d) 8
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 15 (b) 17 (c) 5 (d) 16
  7. 7.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 471 (b) 392 (c) 481 (d) 480
  8. 8.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  9. 9.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 8 (d) 6
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  11. 11.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 162 (c) 144 (d) 153
  12. 12.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
  13. 13.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 5 (b) 6 (c) 8 (d) 7
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 15 (b) 14 (c) 3 (d) 13
  16. 16.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 63 (c) 54 (d) 72
  17. 17.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 4 (b) 7 (c) 5 (d) 6
  19. 19.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 597 (c) 470 (d) 598
  20. 20.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 14 (b) 126 (c) 42 (d) 45
  21. 21.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) 5 (d) 18
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 19 (b) 17 (c) 7 (d) 18
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 9 (b) 19 (c) 18 (d) 20
  24. 24.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 603 (c) 612 (d) 613
  25. 25.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 18 (b) 17 (c) 7 (d) 19
  27. 27.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 157 (c) 158 (d) 166
  28. 28.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 66? (a) 14 (b) 15 (c) 6 (d) 13
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 7 (d) 18
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 19 (b) 8 (c) 18 (d) 20
  32. 32.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 151 (b) 142 (c) 152 (d) 160
  33. 33.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 286 (c) 322 (d) 321
  34. 34.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 21 (c) 66 (d) 63
  35. 35.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) 153 (c) 51 (d) 54
  36. 36.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  37. 37.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 468 (c) 477 (d) 478
  38. 38.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 169 (c) 170 (d) 178
  39. 39.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) 69 (b) 72 (c) 23 (d) 207
  40. 40.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 357 (c) 367 (d) 316

Answer key

  1. 19
  2. 9
  3. 5
  4. 261
  5. 9
  6. 16
  7. 480
  8. 6
  9. 7
  10. 3
  11. 153
  12. 5
  13. 3
  14. 7
  15. 14
  16. 63
  17. 9
  18. 6
  19. 597
  20. 42
  21. 15
  22. 18
  23. 19
  24. 612
  25. 2
  26. 18
  27. 157
  28. 2
  29. 14
  30. 18
  31. 19
  32. 151
  33. 321
  34. 63
  35. 51
  36. 7
  37. 477
  38. 169
  39. 69
  40. 366

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