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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 249 · 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.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 112 (c) 102 (d) 111
  2. 2.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 168 (c) 160 (d) 159
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 19 (d) 18
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 1 (d) 3
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 58? (a) 16 (b) 15 (c) 5 (d) 17
  6. 6.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) 30 (b) 27 (c) 9 (d) 81
  7. 7.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 316 (c) 357 (d) 367
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 5 (b) 4 (c) 3 (d) 2
  9. 9.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) 49 (c) 40 (d) 58
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 10 (d) 6
  11. 11.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 513 (c) 522 (d) 523
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 6 (b) 3 (c) 5 (d) 4
  13. 13.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 326 (b) 382 (c) 381 (d) 372
  14. 14.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 222 (c) 232 (d) 231
  15. 15.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 496 (c) 486 (d) 495
  16. 16.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) 36 (b) 108 (c) 12 (d) 39
  17. 17.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 361 (c) 351 (d) 360
  18. 18.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) 21 (c) 63 (d) 66
  19. 19.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 15 (d) 6
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (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) 126 (b) 45 (c) 42 (d) 14
  22. 22.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  23. 23.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) 162 (b) 18 (c) 57 (d) 54
  24. 24.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 97? (a) 21 (b) 20 (c) 19 (d) 9
  26. 26.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) 15 (c) 135 (d) 48
  27. 27.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 4 (b) 2 (c) 1 (d) 3
  29. 29.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 471 (c) 462 (d) 386
  30. 30.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  31. 31.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) 7 (b) 24 (c) 63 (d) 21
  32. 32.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
  33. 33.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 376 (c) 375 (d) 322
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 19 (b) 20 (c) 9 (d) 21
  35. 35.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 198 (c) 207 (d) 208
  36. 36.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) 153 (b) 54 (c) 17 (d) 51
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 7 (b) 16 (c) 18 (d) 17
  38. 38.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 5 (d) 16
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 18 (b) 16 (c) 6 (d) 17
  40. 40.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 4 (d) 10

Answer key

  1. 111
  2. 159
  3. 18
  4. 3
  5. 16
  6. 27
  7. 366
  8. 4
  9. 49
  10. 7
  11. 522
  12. 5
  13. 381
  14. 231
  15. 495
  16. 36
  17. 360
  18. 63
  19. 5
  20. 4
  21. 42
  22. 6
  23. 54
  24. 8
  25. 20
  26. 45
  27. 6
  28. 3
  29. 471
  30. 2
  31. 21
  32. 8
  33. 375
  34. 20
  35. 207
  36. 51
  37. 17
  38. 4
  39. 17
  40. 3

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