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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 804 · 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 10? (a) 9 (b) 11 (c) 8 (d) 10
  2. 2.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) 48 (c) 57 (d) 58
  3. 3.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 45? (a) 4 (b) 2 (c) 3 (d) 5
  5. 5.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 333 (c) 294 (d) 334
  6. 6.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 475 (c) 388 (d) 465
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 4 (b) 6 (c) 7 (d) 5
  8. 8.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) 54 (b) 17 (c) 51 (d) 153
  9. 9.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 32 (c) 42 (d) 41
  10. 10.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 403 (c) 393 (d) 340
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 21 (d) 19
  12. 12.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) 9 (b) 27 (c) 30 (d) 81
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 17 (b) 18 (c) 7 (d) 19
  14. 14.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 225 (b) 235 (c) 234 (d) 228
  15. 15.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 2 (d) 17
  16. 16.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 540 (c) 541 (d) 432
  17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 6 (b) 5 (c) 3 (d) 4
  18. 18.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  19. 19.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 200 (b) 193 (c) 183 (d) 192
  20. 20.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  21. 21.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) 14 (b) 45 (c) 42 (d) 126
  22. 22.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) 144 (c) 48 (d) 51
  23. 23.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
  24. 24.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
  25. 25.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
  26. 26.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 466 (c) 592 (d) 591
  27. 27.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 20 (b) 180 (c) 60 (d) 63
  28. 28.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 53 (c) 44 (d) 62
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 18 (b) 6 (c) 16 (d) 17
  30. 30.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 124 (c) 106 (d) 115
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 8 (b) 9 (c) 10 (d) 11
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 5 (b) 3 (c) 4 (d) 2
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 18 (b) 17 (c) 7 (d) 16
  34. 34.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 72 (c) 81 (d) 82
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 19 (b) 20 (c) 21 (d) 9
  36. 36.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 18 (b) 17 (c) 7 (d) 19
  38. 38.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  39. 39.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 165 (c) 174 (d) 156
  40. 40.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) 382 (c) 381 (d) 326

Answer key

  1. 9
  2. 57
  3. 4
  4. 4
  5. 333
  6. 474
  7. 6
  8. 51
  9. 41
  10. 402
  11. 20
  12. 27
  13. 18
  14. 234
  15. 3
  16. 540
  17. 5
  18. 7
  19. 192
  20. 3
  21. 42
  22. 48
  23. 5
  24. 6
  25. 2
  26. 591
  27. 60
  28. 53
  29. 17
  30. 115
  31. 10
  32. 4
  33. 17
  34. 81
  35. 20
  36. 9
  37. 18
  38. 4
  39. 165
  40. 381

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