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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 841 · 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 32? (a) 2 (b) 4 (c) 3 (d) 1
  2. 2.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 100 (c) 109 (d) 110
  3. 3.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) 180 (b) 20 (c) 60 (d) 63
  4. 4.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 166 (c) 175 (d) 184
  5. 5.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 16 (b) 15 (c) 5 (d) 17
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 4 (b) 3 (c) 1 (d) 2
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 13 (b) 15 (c) 14 (d) 4
  9. 9.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 39 (c) 30 (d) 48
  10. 10.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) 54 (b) 51 (c) 153 (d) 17
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 14 (b) 15 (c) 4 (d) 16
  12. 12.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 20 (b) 9 (c) 21 (d) 19
  14. 14.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1
  15. 15.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 20 (b) 18 (c) 19 (d) 9
  17. 17.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 470 (c) 598 (d) 597
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 15 (b) 13 (c) 3 (d) 14
  19. 19.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 61 (b) 62 (c) 52 (d) 70
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 99? (a) 21 (b) 20 (c) 9 (d) 19
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 15 (b) 14 (c) 4 (d) 16
  22. 22.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) 15 (b) 5 (c) 18 (d) 45
  23. 23.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 2 (b) 3 (c) 5 (d) 4
  25. 25.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 366 (c) 375 (d) 376
  26. 26.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) 135 (b) 45 (c) 48 (d) 15
  27. 27.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 388 (c) 475 (d) 474
  28. 28.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) 189 (c) 63 (d) 66
  29. 29.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) 216 (c) 24 (d) 72
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 8 (b) 11 (c) 10 (d) 5
  31. 31.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  32. 32.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 76 (c) 85 (d) 86
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 5 (b) 6 (c) 4 (d) 3
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 8 (d) 19
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 15 (b) 5 (c) 17 (d) 16
  36. 36.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) 72 (c) 27 (d) 24
  37. 37.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 149 (b) 140 (c) 158 (d) 150
  38. 38.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  39. 39.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 117 (c) 108 (d) 118
  40. 40.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 216 (c) 226 (d) 225

Answer key

  1. 3
  2. 109
  3. 60
  4. 175
  5. 5
  6. 16
  7. 3
  8. 14
  9. 39
  10. 51
  11. 15
  12. 4
  13. 20
  14. 2
  15. 3
  16. 19
  17. 597
  18. 14
  19. 61
  20. 20
  21. 15
  22. 15
  23. 7
  24. 4
  25. 375
  26. 45
  27. 474
  28. 63
  29. 72
  30. 10
  31. 9
  32. 85
  33. 5
  34. 19
  35. 16
  36. 24
  37. 149
  38. 3
  39. 117
  40. 225

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