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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 399 · 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) 504 (b) 408 (c) 495 (d) 505
  2. 2.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  3. 3.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) 45 (b) 42 (c) 14 (d) 126
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 19 (b) 7 (c) 18 (d) 17
  5. 5.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 307 (c) 306 (d) 297
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 16 (b) 18 (c) 6 (d) 17
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 5 (b) 4 (c) 3 (d) 2
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 14 (b) 15 (c) 5 (d) 16
  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) 16 (b) 51 (c) 144 (d) 48
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 4 (b) 15 (c) 16 (d) 14
  12. 12.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 346 (c) 402 (d) 412
  13. 13.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) 117 (d) 13
  14. 14.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 8 (b) 18 (c) 20 (d) 19
  16. 16.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 636 (b) 637 (c) 627 (d) 496
  17. 17.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 163 (b) 172 (c) 164 (d) 154
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 80? (a) 10 (b) 7 (c) 9 (d) 8
  19. 19.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) 367 (c) 357 (d) 316
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 12 (b) 13 (c) 3 (d) 11
  21. 21.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) 10 (b) 30 (c) 33 (d) 90
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 11 (b) 10 (c) 8 (d) 5
  23. 23.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) 36 (c) 12 (d) 39
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 9 (d) 21
  25. 25.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 62 (c) 52 (d) 61
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 6 (b) 8 (c) 7 (d) 5
  27. 27.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) 36 (b) 33 (c) 11 (d) 99
  28. 28.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 30 (c) 81 (d) 9
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 18 (b) 7 (c) 19 (d) 17
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 3 (b) 4 (c) 1 (d) 2
  31. 31.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) 8 (b) 24 (c) 72 (d) 27
  32. 32.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 98 (c) 97 (d) 88
  33. 33.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 99? (a) 20 (b) 9 (c) 21 (d) 19
  35. 35.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 507 (c) 416 (d) 517
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 5 (b) 6 (c) 7 (d) 8
  37. 37.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 422 (c) 525 (d) 526
  38. 38.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 202 (b) 195 (c) 196 (d) 186
  39. 39.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 8 (d) 7
  40. 40.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) 54 (c) 6 (d) 21

Answer key

  1. 504
  2. 4
  3. 42
  4. 18
  5. 306
  6. 9
  7. 17
  8. 4
  9. 15
  10. 48
  11. 15
  12. 411
  13. 39
  14. 2
  15. 19
  16. 636
  17. 163
  18. 9
  19. 366
  20. 12
  21. 30
  22. 10
  23. 36
  24. 20
  25. 61
  26. 7
  27. 33
  28. 27
  29. 18
  30. 3
  31. 24
  32. 97
  33. 2
  34. 20
  35. 516
  36. 7
  37. 525
  38. 195
  39. 8
  40. 18

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