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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 904 · 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 44? (a) 3 (b) 5 (c) 4 (d) 2
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 14 (b) 15 (c) 3 (d) 13
  3. 3.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) 57 (b) 162 (c) 54 (d) 18
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 4 (d) 10
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 92? (a) 20 (b) 18 (c) 9 (d) 19
  6. 6.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  7. 7.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) 27 (c) 72 (d) 24
  8. 8.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) 58 (c) 40 (d) 49
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 4 (b) 7 (c) 5 (d) 6
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 14 (b) 15 (c) 3 (d) 13
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 54? (a) 4 (b) 5 (c) 6 (d) 3
  12. 12.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) 171 (b) 19 (c) 57 (d) 60
  13. 13.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 468 (c) 595 (d) 594
  14. 14.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) 207 (b) 72 (c) 69 (d) 23
  15. 15.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7
  16. 16.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 198 (c) 180 (d) 189
  17. 17.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 201 (c) 202 (d) 206
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 2 (b) 3 (c) 4 (d) 5
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 4 (b) 2 (c) 3 (d) 5
  20. 20.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) 39 (b) 117 (c) 42 (d) 13
  21. 21.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 385 (b) 384 (c) 375 (d) 328
  22. 22.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 62 (c) 54 (d) 53
  23. 23.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 397 (c) 336 (d) 387
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 10 (b) 5 (c) 9 (d) 7
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 6 (b) 15 (c) 17 (d) 16
  26. 26.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 15 (c) 5 (d) 45
  27. 27.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 18 (b) 7 (c) 19 (d) 17
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 19 (b) 18 (c) 17 (d) 7
  30. 30.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 8 (b) 18 (c) 20 (d) 19
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 16 (b) 6 (c) 17 (d) 18
  33. 33.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 189 (c) 199 (d) 198
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 85? (a) 8 (b) 18 (c) 19 (d) 20
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 5 (b) 3 (c) 4 (d) 6
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 5 (b) 17 (c) 16 (d) 15
  37. 37.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 408 (c) 417 (d) 350
  38. 38.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  39. 39.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 194 (c) 186 (d) 185
  40. 40.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 576 (c) 586 (d) 585

Answer key

  1. 4
  2. 14
  3. 54
  4. 3
  5. 19
  6. 6
  7. 24
  8. 49
  9. 6
  10. 14
  11. 5
  12. 57
  13. 594
  14. 69
  15. 7
  16. 189
  17. 201
  18. 4
  19. 4
  20. 39
  21. 384
  22. 53
  23. 396
  24. 9
  25. 16
  26. 15
  27. 4
  28. 18
  29. 18
  30. 3
  31. 19
  32. 17
  33. 198
  34. 19
  35. 5
  36. 16
  37. 417
  38. 2
  39. 185
  40. 585

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