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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 325 · 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 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) 54 (d) 18
  2. 2.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 298 (c) 340 (d) 339
  3. 3.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 396 (c) 406 (d) 342
  4. 4.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 7 (d) 9
  5. 5.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) 11 (b) 36 (c) 99 (d) 33
  6. 6.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) 207 (b) 72 (c) 69 (d) 23
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 8 (b) 5 (c) 6 (d) 7
  8. 8.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 304 (c) 348 (d) 339
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 6 (b) 8 (c) 9 (d) 7
  10. 10.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 17 (b) 7 (c) 19 (d) 18
  12. 12.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) 45 (c) 15 (d) 5
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 17 (d) 7
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 14 (b) 13 (c) 12 (d) 3
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 14 (b) 15 (c) 16 (d) 5
  16. 16.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 358 (c) 357 (d) 310
  17. 17.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
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 5 (b) 6 (c) 3 (d) 4
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 6 (b) 17 (c) 15 (d) 16
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 3 (b) 6 (c) 4 (d) 5
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 15 (b) 17 (c) 6 (d) 16
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 5 (b) 4 (c) 2 (d) 3
  23. 23.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 454 (c) 564 (d) 574
  24. 24.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 141 (c) 150 (d) 132
  25. 25.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 474 (c) 484 (d) 394
  26. 26.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) 21 (b) 63 (c) 189 (d) 66
  27. 27.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) 42 (b) 14 (c) 126 (d) 45
  28. 28.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 418 (c) 520 (d) 519
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 95? (a) 18 (b) 20 (c) 19 (d) 9
  30. 30.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) 613 (c) 612 (d) 603
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 7 (b) 5 (c) 8 (d) 6
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 1 (b) 4 (c) 2 (d) 3
  33. 33.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 439 (c) 438 (d) 364
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 17 (b) 16 (c) 7 (d) 18
  35. 35.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  36. 36.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) 66 (c) 76 (d) 84
  37. 37.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 133 (c) 134 (d) 124
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 14 (b) 13 (c) 15 (d) 3
  39. 39.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 8 (b) 5 (c) 6 (d) 7

Answer key

  1. 54
  2. 339
  3. 405
  4. 8
  5. 33
  6. 69
  7. 7
  8. 348
  9. 8
  10. 8
  11. 18
  12. 15
  13. 18
  14. 13
  15. 15
  16. 357
  17. 72
  18. 5
  19. 16
  20. 5
  21. 16
  22. 4
  23. 573
  24. 141
  25. 483
  26. 63
  27. 42
  28. 519
  29. 19
  30. 612
  31. 7
  32. 3
  33. 438
  34. 17
  35. 5
  36. 75
  37. 133
  38. 14
  39. 4
  40. 7

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