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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 275 · 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 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 595 (c) 594 (d) 585
  2. 2.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) 21 (c) 24 (d) 63
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 3 (d) 2
  5. 5.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) 14 (c) 42 (d) 45
  6. 6.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 8 (d) 18
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 86? (a) 20 (b) 8 (c) 19 (d) 18
  9. 9.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 433 (b) 432 (c) 360 (d) 423
  10. 10.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  11. 11.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) 30 (b) 10 (c) 90 (d) 33
  12. 12.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) 75 (b) 24 (c) 72 (d) 216
  13. 13.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) 21 (b) 63 (c) 66 (d) 189
  14. 14.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 54 (c) 45 (d) 46
  15. 15.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) 81 (b) 30 (c) 9 (d) 27
  16. 16.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 460 (c) 459 (d) 378
  17. 17.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 404 (c) 499 (d) 498
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 7 (b) 18 (c) 17 (d) 16
  19. 19.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 88 (c) 78 (d) 87
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 4 (b) 14 (c) 15 (d) 13
  21. 21.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  22. 22.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 19 (b) 17 (c) 7 (d) 18
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 15 (b) 16 (c) 17 (d) 5
  25. 25.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 459 (c) 468 (d) 469
  26. 26.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 504 (c) 505 (d) 408
  27. 27.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 438 (c) 448 (d) 447
  28. 28.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 286 (c) 285 (d) 262
  29. 29.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 294 (c) 304 (d) 274
  30. 30.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
  31. 31.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) 60 (b) 20 (c) 63 (d) 180
  32. 32.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 107 (b) 108 (c) 116 (d) 98
  33. 33.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 75 (c) 66 (d) 76
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 2 (b) 1 (c) 4 (d) 3
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 54? (a) 15 (b) 17 (c) 5 (d) 16
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 32? (a) 4 (b) 3 (c) 2 (d) 1
  37. 37.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) 54 (c) 17 (d) 153
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 5 (b) 4 (c) 2 (d) 3
  39. 39.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 199 (c) 198 (d) 204
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 19 (b) 18 (c) 8 (d) 17

Answer key

  1. 594
  2. 21
  3. 2
  4. 3
  5. 42
  6. 7
  7. 18
  8. 19
  9. 432
  10. 5
  11. 30
  12. 72
  13. 63
  14. 45
  15. 27
  16. 459
  17. 498
  18. 17
  19. 87
  20. 14
  21. 4
  22. 6
  23. 18
  24. 16
  25. 468
  26. 504
  27. 447
  28. 285
  29. 303
  30. 57
  31. 60
  32. 107
  33. 75
  34. 3
  35. 16
  36. 3
  37. 51
  38. 4
  39. 198
  40. 18

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