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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 488 · 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 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 152 (c) 143 (d) 134
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 4 (b) 3 (c) 2 (d) 5
  4. 4.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 147 (b) 148 (c) 138 (d) 156
  5. 5.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 77 (c) 68 (d) 86
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  7. 7.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 537 (b) 546 (c) 436 (d) 547
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 19 (d) 20
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 6 (b) 5 (c) 7 (d) 4
  10. 10.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) 90 (b) 33 (c) 30 (d) 10
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 9 (b) 20 (c) 21 (d) 19
  12. 12.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) 63 (b) 24 (c) 21 (d) 7
  13. 13.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 380 (b) 462 (c) 453 (d) 463
  14. 14.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) 24 (b) 72 (c) 8 (d) 27
  15. 15.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  16. 16.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 482 (c) 616 (d) 615
  17. 17.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) 42 (b) 117 (c) 39 (d) 13
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 7 (b) 19 (c) 18 (d) 17
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 16 (b) 7 (c) 17 (d) 18
  20. 20.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) 144 (b) 16 (c) 51 (d) 48
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 8 (b) 18 (c) 17 (d) 19
  22. 22.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) 33 (c) 11 (d) 36
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  24. 24.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) 54 (b) 162 (c) 18 (d) 57
  25. 25.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 327 (c) 337 (d) 296
  26. 26.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 198 (c) 180 (d) 189
  27. 27.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 15 (b) 17 (c) 16 (d) 6
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 63? (a) 4 (b) 6 (c) 7 (d) 5
  30. 30.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 476 (b) 606 (c) 607 (d) 597
  31. 31.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  32. 32.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 366 (c) 441 (d) 432
  33. 33.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 126 (c) 134 (d) 125
  34. 34.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  35. 35.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  36. 36.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 15 (b) 4 (c) 13 (d) 14
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 16 (b) 7 (c) 17 (d) 18
  39. 39.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 276 (c) 262 (d) 285
  40. 40.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 487 (c) 486 (d) 396

Answer key

  1. 143
  2. 9
  3. 4
  4. 147
  5. 77
  6. 2
  7. 546
  8. 20
  9. 6
  10. 30
  11. 20
  12. 21
  13. 462
  14. 24
  15. 8
  16. 615
  17. 39
  18. 18
  19. 17
  20. 48
  21. 18
  22. 33
  23. 3
  24. 54
  25. 336
  26. 189
  27. 5
  28. 16
  29. 6
  30. 606
  31. 5
  32. 441
  33. 125
  34. 9
  35. 8
  36. 3
  37. 14
  38. 17
  39. 285
  40. 486

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