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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 988 · 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 46? (a) 15 (b) 16 (c) 14 (d) 4
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 18 (b) 15 (c) 9 (d) 17
  3. 3.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  4. 4.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) 69 (b) 207 (c) 23 (d) 72
  5. 5.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  6. 6.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) 5 (b) 45 (c) 18 (d) 15
  7. 7.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 26 (c) 35 (d) 36
  8. 8.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 392 (b) 471 (c) 481 (d) 480
  9. 9.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 153 (b) 162 (c) 144 (d) 154
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 7 (b) 9 (c) 6 (d) 8
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 3 (b) 4 (c) 5 (d) 6
  12. 12.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) 18 (c) 162 (d) 54
  13. 13.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 568 (c) 558 (d) 450
  14. 14.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) 42 (b) 117 (c) 13 (d) 39
  15. 15.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) 363 (c) 320 (d) 372
  16. 16.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 277 (c) 256 (d) 276
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 5 (b) 4 (c) 6 (d) 7
  18. 18.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) 42 (b) 14 (c) 126 (d) 45
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 17 (d) 8
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 96? (a) 14 (b) 9 (c) 16 (d) 17
  21. 21.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) 45 (c) 48 (d) 135
  22. 22.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 477 (c) 390 (d) 478
  23. 23.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 75 (b) 84 (c) 76 (d) 66
  24. 24.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 356 (b) 427 (c) 417 (d) 426
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 3 (b) 10 (c) 11 (d) 12
  26. 26.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) 27 (c) 30 (d) 9
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 54? (a) 16 (b) 5 (c) 15 (d) 17
  28. 28.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 474 (c) 604 (d) 603
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 21 (b) 19 (c) 9 (d) 20
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 16 (b) 14 (c) 15 (d) 4
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 17 (b) 6 (c) 18 (d) 16
  32. 32.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  33. 33.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 36 (c) 11 (d) 33
  34. 34.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) 24 (b) 63 (c) 7 (d) 21
  35. 35.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  36. 36.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) 12 (b) 108 (c) 36 (d) 39
  37. 37.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 595 (b) 585 (c) 594 (d) 468
  38. 38.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 62 (c) 71 (d) 80
  39. 39.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 120 (c) 111 (d) 102
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 5 (b) 16 (c) 14 (d) 15

Answer key

  1. 15
  2. 17
  3. 5
  4. 69
  5. 2
  6. 15
  7. 35
  8. 480
  9. 153
  10. 8
  11. 5
  12. 54
  13. 567
  14. 39
  15. 372
  16. 276
  17. 6
  18. 42
  19. 18
  20. 16
  21. 45
  22. 477
  23. 75
  24. 426
  25. 11
  26. 27
  27. 16
  28. 603
  29. 20
  30. 15
  31. 17
  32. 7
  33. 33
  34. 21
  35. 5
  36. 36
  37. 594
  38. 71
  39. 111
  40. 15

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