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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 410 · 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 8? (a) 7 (b) 9 (c) 10 (d) 8
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  3. 3.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) 72 (c) 24 (d) 27
  4. 4.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 40 (c) 58 (d) 49
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 3 (b) 4 (c) 5 (d) 6
  6. 6.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 100 (c) 82 (d) 91
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 20 (b) 19 (c) 9 (d) 21
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18
  9. 9.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  10. 10.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 576 (c) 462 (d) 586
  11. 11.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) 126 (c) 45 (d) 14
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 51? (a) 14 (b) 5 (c) 16 (d) 15
  13. 13.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 177 (c) 186 (d) 168
  14. 14.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 282 (c) 283 (d) 260
  15. 15.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 76 (c) 85 (d) 86
  16. 16.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) 153 (d) 54
  17. 17.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 230 (b) 228 (c) 237 (d) 238
  18. 18.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) 45 (b) 135 (c) 48 (d) 15
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 7 (b) 5 (c) 6 (d) 4
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 7 (b) 5 (c) 4 (d) 8
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 58? (a) 7 (b) 5 (c) 4 (d) 6
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  23. 23.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 490 (c) 628 (d) 627
  24. 24.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  25. 25.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 298 (c) 288 (d) 270
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 5 (b) 4 (c) 3 (d) 2
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 20 (b) 18 (c) 8 (d) 19
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 4 (b) 7 (c) 5 (d) 6
  29. 29.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 339 (c) 349 (d) 348
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 13 (b) 15 (c) 14 (d) 3
  31. 31.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 465 (c) 456 (d) 382
  32. 32.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 17 (b) 16 (c) 15 (d) 5
  34. 34.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 606 (c) 607 (d) 476
  35. 35.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 60 (c) 78 (d) 69
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 9 (b) 6 (c) 8 (d) 7
  37. 37.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 102 (c) 92 (d) 101
  38. 38.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 579 (c) 580 (d) 458
  39. 39.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) 57 (c) 162 (d) 18
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 4 (b) 1 (c) 3 (d) 2

Answer key

  1. 8
  2. 9
  3. 24
  4. 49
  5. 5
  6. 91
  7. 20
  8. 19
  9. 9
  10. 585
  11. 42
  12. 15
  13. 177
  14. 282
  15. 85
  16. 51
  17. 237
  18. 45
  19. 6
  20. 7
  21. 6
  22. 3
  23. 627
  24. 6
  25. 297
  26. 4
  27. 19
  28. 6
  29. 348
  30. 14
  31. 465
  32. 2
  33. 16
  34. 606
  35. 69
  36. 8
  37. 101
  38. 579
  39. 54
  40. 3

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