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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 874 · 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 9 written when you write all the numbers from 1 to 90? (a) 11 (b) 9 (c) 8 (d) 10
  2. 2.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) 24 (b) 72 (c) 8 (d) 27
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 20 (d) 9
  4. 4.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 373 (b) 320 (c) 372 (d) 363
  5. 5.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) 60 (b) 171 (c) 57 (d) 19
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 5 (b) 2 (c) 3 (d) 4
  7. 7.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 571 (c) 561 (d) 452
  8. 8.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) 13 (b) 42 (c) 39 (d) 117
  9. 9.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 10 (c) 30 (d) 33
  10. 10.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
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 18 (b) 19 (c) 20 (d) 8
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 15 (b) 3 (c) 14 (d) 13
  13. 13.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  14. 14.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  15. 15.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 300 (c) 278 (d) 309
  16. 16.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 19 (b) 20 (c) 21 (d) 9
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 21 (b) 20 (c) 19 (d) 9
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 5 (d) 4
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 15 (b) 16 (c) 6 (d) 17
  21. 21.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  22. 22.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 276 (c) 285 (d) 262
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 95? (a) 19 (b) 18 (c) 20 (d) 9
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 16 (b) 6 (c) 17 (d) 18
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  26. 26.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 2 (b) 1 (c) 3 (d) 4
  28. 28.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 330 (c) 298 (d) 340
  29. 29.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 187 (b) 188 (c) 196 (d) 178
  30. 30.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 484 (c) 394 (d) 483
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 15 (b) 5 (c) 16 (d) 17
  32. 32.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) 51 (b) 153 (c) 54 (d) 17
  33. 33.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 43 (c) 52 (d) 44
  34. 34.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 86 (c) 95 (d) 104
  35. 35.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  36. 36.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 216 (c) 75 (d) 24
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 9 (b) 12 (c) 13 (d) 10
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 16 (b) 7 (c) 17 (d) 18
  39. 39.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 69 (c) 207 (d) 23
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 3 (b) 15 (c) 13 (d) 14

Answer key

  1. 10
  2. 24
  3. 20
  4. 372
  5. 57
  6. 4
  7. 570
  8. 39
  9. 30
  10. 27
  11. 19
  12. 14
  13. 9
  14. 3
  15. 309
  16. 5
  17. 20
  18. 20
  19. 5
  20. 16
  21. 6
  22. 285
  23. 19
  24. 17
  25. 7
  26. 3
  27. 3
  28. 339
  29. 187
  30. 483
  31. 16
  32. 51
  33. 43
  34. 95
  35. 2
  36. 72
  37. 12
  38. 17
  39. 69
  40. 14

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