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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 144 · 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 two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  2. 2.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 110 (c) 118 (d) 109
  3. 3.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  4. 4.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 338 (c) 399 (d) 390
  5. 5.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  6. 6.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) 6 (b) 54 (c) 18 (d) 21
  7. 7.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 457 (c) 447 (d) 376
  8. 8.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  9. 9.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 3 (b) 2 (c) 4 (d) 5
  11. 11.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 57 (c) 48 (d) 58
  12. 12.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 102 (c) 93 (d) 94
  13. 13.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) 66 (b) 63 (c) 189 (d) 21
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 8 (b) 9 (c) 7 (d) 6
  15. 15.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 8 (b) 19 (c) 17 (d) 18
  17. 17.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) 152 (c) 134 (d) 144
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 18 (b) 17 (c) 8 (d) 19
  19. 19.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 442 (c) 432 (d) 441
  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) 42 (b) 45 (c) 14 (d) 126
  21. 21.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 379 (c) 324 (d) 378
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 8 (b) 6 (c) 7 (d) 9
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 99? (a) 9 (b) 19 (c) 20 (d) 21
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 3 (b) 5 (c) 4 (d) 6
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 83? (a) 18 (b) 19 (c) 8 (d) 20
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 3 (b) 13 (c) 15 (d) 14
  27. 27.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
  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) 9 (d) 81
  29. 29.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 70 (c) 62 (d) 61
  30. 30.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 199 (b) 198 (c) 204 (d) 189
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 95? (a) 18 (b) 20 (c) 9 (d) 19
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 21 (b) 19 (c) 9 (d) 20
  33. 33.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  34. 34.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 228 (c) 229 (d) 224
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 55? (a) 16 (b) 15 (c) 17 (d) 5
  36. 36.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) 12 (b) 36 (c) 108 (d) 39
  37. 37.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 372 (c) 382 (d) 326
  38. 38.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4
  39. 39.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9
  40. 40.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 189 (c) 190 (d) 198

Answer key

  1. 6
  2. 109
  3. 5
  4. 399
  5. 9
  6. 18
  7. 456
  8. 4
  9. 7
  10. 4
  11. 57
  12. 93
  13. 63
  14. 8
  15. 7
  16. 18
  17. 143
  18. 18
  19. 441
  20. 42
  21. 378
  22. 8
  23. 20
  24. 5
  25. 19
  26. 14
  27. 69
  28. 27
  29. 61
  30. 198
  31. 19
  32. 20
  33. 3
  34. 228
  35. 16
  36. 36
  37. 381
  38. 4
  39. 8
  40. 189

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