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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 226 · 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 4 written when you write all the numbers from 1 to 30? (a) 3 (b) 4 (c) 1 (d) 2
  2. 2.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 8 (b) 19 (c) 20 (d) 18
  4. 4.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 456 (c) 466 (d) 465
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 20 (b) 9 (c) 21 (d) 19
  6. 6.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  7. 7.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 243 (c) 252 (d) 253
  8. 8.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 396 (c) 397 (d) 336
  9. 9.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) 10 (c) 33 (d) 30
  10. 10.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 193 (b) 183 (c) 192 (d) 200
  11. 11.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 372 (c) 373 (d) 320
  12. 12.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 324 (c) 294 (d) 333
  13. 13.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) 7 (d) 21
  14. 14.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  15. 15.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
  16. 16.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 45 (c) 135 (d) 15
  17. 17.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 140 (c) 132 (d) 131
  18. 18.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 18 (b) 6 (c) 16 (d) 17
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  21. 21.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  22. 22.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 85 (c) 94 (d) 76
  23. 23.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) 526 (c) 422 (d) 525
  24. 24.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 111 (b) 120 (c) 102 (d) 112
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 16 (b) 7 (c) 18 (d) 17
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 8 (b) 17 (c) 18 (d) 19
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 20 (b) 8 (c) 19 (d) 18
  28. 28.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
  29. 29.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 115 (b) 124 (c) 116 (d) 106
  30. 30.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  31. 31.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  32. 32.The numbers 18 to 26 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) 69 (c) 198 (d) 22
  33. 33.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  34. 34.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  35. 35.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 403 (b) 402 (c) 340 (d) 393
  36. 36.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  37. 37.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 108 (c) 117 (d) 118
  38. 38.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) 39 (c) 108 (d) 36
  39. 39.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 33 (c) 42 (d) 34
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 20 (b) 18 (c) 8 (d) 19

Answer key

  1. 3
  2. 5
  3. 19
  4. 465
  5. 20
  6. 7
  7. 252
  8. 396
  9. 30
  10. 192
  11. 372
  12. 333
  13. 21
  14. 9
  15. 6
  16. 45
  17. 131
  18. 8
  19. 17
  20. 4
  21. 8
  22. 85
  23. 525
  24. 111
  25. 17
  26. 18
  27. 19
  28. 348
  29. 115
  30. 7
  31. 3
  32. 66
  33. 5
  34. 9
  35. 402
  36. 4
  37. 117
  38. 36
  39. 33
  40. 19

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