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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 801 · 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 69? (a) 16 (b) 18 (c) 17 (d) 6
  2. 2.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 51 (c) 54 (d) 153
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 7 (b) 6 (c) 4 (d) 5
  4. 4.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 249 (c) 259 (d) 258
  5. 5.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  6. 6.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) 21 (c) 24 (d) 7
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 16 (b) 6 (c) 18 (d) 17
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 19 (b) 17 (c) 18 (d) 8
  9. 9.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) 48 (c) 16 (d) 51
  10. 10.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  11. 11.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) 117 (c) 13 (d) 42
  12. 12.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 7 (d) 5
  13. 13.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 171 (c) 60 (d) 57
  14. 14.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 387 (c) 397 (d) 396
  15. 15.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 9 (d) 7
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 13 (b) 15 (c) 14 (d) 3
  17. 17.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 60 (c) 50 (d) 59
  18. 18.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 211 (b) 210 (c) 201 (d) 212
  19. 19.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 499 (c) 489 (d) 404
  20. 20.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  21. 21.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) 81 (b) 30 (c) 27 (d) 9
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 6 (d) 10
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 18 (d) 19
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 3 (b) 5 (c) 6 (d) 4
  25. 25.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 381 (c) 326 (d) 382
  26. 26.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) 253 (c) 243 (d) 252
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 1 (d) 2
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 20 (b) 18 (c) 8 (d) 19
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 8 (b) 18 (c) 20 (d) 19
  30. 30.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  31. 31.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 325 (c) 324 (d) 288
  32. 32.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 107 (c) 98 (d) 116
  33. 33.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 180 (c) 179 (d) 170
  34. 34.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 564 (c) 448 (d) 565
  35. 35.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
  36. 36.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 16 (b) 4 (c) 14 (d) 15
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 5 (b) 2 (c) 3 (d) 4
  39. 39.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 391 (b) 381 (c) 390 (d) 332
  40. 40.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 410 (b) 508 (c) 507 (d) 498

Answer key

  1. 17
  2. 51
  3. 6
  4. 258
  5. 7
  6. 21
  7. 17
  8. 18
  9. 48
  10. 9
  11. 39
  12. 6
  13. 57
  14. 396
  15. 8
  16. 14
  17. 59
  18. 210
  19. 498
  20. 8
  21. 27
  22. 5
  23. 19
  24. 5
  25. 381
  26. 252
  27. 3
  28. 19
  29. 19
  30. 4
  31. 324
  32. 107
  33. 179
  34. 564
  35. 3
  36. 5
  37. 15
  38. 4
  39. 390
  40. 507

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