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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 729 · 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 1 written when you write all the numbers from 1 to 96? (a) 21 (b) 19 (c) 20 (d) 9
  2. 2.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 216 (d) 225
  3. 3.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  4. 4.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) 607 (c) 476 (d) 606
  5. 5.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 308 (b) 354 (c) 345 (d) 355
  6. 6.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 159 (b) 150 (c) 168 (d) 160
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 4 (b) 11 (c) 12 (d) 10
  8. 8.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) 15 (b) 135 (c) 45 (d) 48
  9. 9.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) 60 (c) 180 (d) 63
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 3 (b) 4 (c) 6 (d) 5
  11. 11.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) 57 (b) 60 (c) 171 (d) 19
  12. 12.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) 189 (b) 63 (c) 21 (d) 66
  13. 13.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) 126 (b) 45 (c) 14 (d) 42
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 6 (b) 7 (c) 5 (d) 4
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 3 (d) 1
  16. 16.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  17. 17.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  18. 18.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 426 (c) 362 (d) 435
  19. 19.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 149 (b) 158 (c) 140 (d) 150
  20. 20.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
  21. 21.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 82 (c) 90 (d) 81
  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) 144 (b) 48 (c) 16 (d) 51
  23. 23.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 216 (c) 207 (d) 217
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 19 (b) 9 (c) 20 (d) 21
  25. 25.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  26. 26.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 17 (b) 6 (c) 18 (d) 16
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 60? (a) 6 (b) 16 (c) 15 (d) 17
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 10 (d) 6
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 6 (b) 7 (c) 4 (d) 3
  31. 31.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 420 (c) 523 (d) 522
  32. 32.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 15 (b) 6 (c) 17 (d) 16
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 58? (a) 5 (b) 4 (c) 7 (d) 6
  35. 35.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 519 (c) 520 (d) 418
  36. 36.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 468 (c) 477 (d) 390
  37. 37.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) 22 (b) 66 (c) 69 (d) 198
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 7 (b) 18 (c) 17 (d) 19
  39. 39.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  40. 40.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 138 (c) 120 (d) 129

Answer key

  1. 20
  2. 225
  3. 2
  4. 606
  5. 354
  6. 159
  7. 11
  8. 45
  9. 60
  10. 5
  11. 57
  12. 63
  13. 42
  14. 6
  15. 3
  16. 9
  17. 4
  18. 435
  19. 149
  20. 6
  21. 81
  22. 48
  23. 216
  24. 20
  25. 9
  26. 7
  27. 17
  28. 16
  29. 7
  30. 6
  31. 522
  32. 6
  33. 16
  34. 6
  35. 519
  36. 477
  37. 66
  38. 18
  39. 5
  40. 129

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