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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 788 · 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 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 367 (b) 357 (c) 316 (d) 366
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 9 (d) 20
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  4. 4.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) 45 (b) 18 (c) 5 (d) 15
  5. 5.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 158 (c) 149 (d) 140
  6. 6.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) 17 (b) 54 (c) 153 (d) 51
  7. 7.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 114 (c) 105 (d) 106
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 4 (b) 7 (c) 5 (d) 6
  9. 9.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 50 (c) 42 (d) 41
  10. 10.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 132 (c) 141 (d) 150
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 3 (b) 12 (c) 14 (d) 13
  13. 13.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 21 (c) 18 (d) 6
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  15. 15.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 397 (b) 336 (c) 396 (d) 387
  16. 16.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) 102 (d) 111
  17. 17.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 549 (c) 540 (d) 550
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 17 (b) 16 (c) 18 (d) 7
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 77? (a) 5 (b) 8 (c) 7 (d) 6
  20. 20.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) 10 (b) 30 (c) 33 (d) 90
  21. 21.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 11 (d) 8
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 7 (b) 17 (c) 19 (d) 18
  23. 23.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) 21 (b) 24 (c) 63 (d) 7
  24. 24.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 487 (b) 396 (c) 477 (d) 486
  25. 25.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 476 (b) 606 (c) 607 (d) 597
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 16 (d) 5
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 3 (b) 5 (c) 4 (d) 2
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 7 (b) 15 (c) 17 (d) 16
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 15 (d) 14
  30. 30.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 404 (b) 499 (c) 498 (d) 489
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 18 (b) 19 (c) 20 (d) 8
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 7 (b) 10 (c) 5 (d) 9
  33. 33.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  34. 34.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) 48 (c) 135 (d) 45
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 15 (b) 16 (c) 6 (d) 17
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 13 (b) 3 (c) 14 (d) 15
  37. 37.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) 27 (b) 8 (c) 72 (d) 24
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 1 (b) 3 (c) 4 (d) 2
  39. 39.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 92 (c) 100 (d) 91
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 15 (b) 12 (c) 14 (d) 7

Answer key

  1. 366
  2. 20
  3. 2
  4. 15
  5. 149
  6. 51
  7. 105
  8. 6
  9. 41
  10. 141
  11. 3
  12. 13
  13. 18
  14. 7
  15. 396
  16. 111
  17. 549
  18. 17
  19. 7
  20. 30
  21. 9
  22. 18
  23. 21
  24. 486
  25. 606
  26. 16
  27. 4
  28. 16
  29. 15
  30. 498
  31. 19
  32. 9
  33. 4
  34. 45
  35. 16
  36. 14
  37. 24
  38. 3
  39. 91
  40. 14

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