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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 21 · 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 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 157 (b) 166 (c) 148 (d) 158
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 7 (b) 18 (c) 19 (d) 17
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 17 (b) 16 (c) 6 (d) 18
  4. 4.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 280 (c) 258 (d) 279
  5. 5.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) 72 (b) 27 (c) 24 (d) 8
  6. 6.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) 60 (b) 57 (c) 171 (d) 19
  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) 106 (b) 105 (c) 114 (d) 96
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9
  9. 9.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) 86 (c) 85 (d) 76
  10. 10.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 17 (b) 18 (c) 7 (d) 19
  12. 12.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 330 (c) 339 (d) 298
  13. 13.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 471 (c) 481 (d) 392
  14. 14.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) 66 (b) 189 (c) 21 (d) 63
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 20 (b) 19 (c) 18 (d) 9
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 15 (b) 3 (c) 14 (d) 13
  17. 17.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 154 (c) 144 (d) 153
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 58? (a) 15 (b) 17 (c) 16 (d) 5
  19. 19.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) 45 (b) 14 (c) 42 (d) 126
  20. 20.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) 48 (c) 15 (d) 45
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 16 (b) 17 (c) 18 (d) 6
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  23. 23.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 3 (b) 6 (c) 4 (d) 5
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 4 (b) 3 (c) 1 (d) 2
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 17 (b) 8 (c) 18 (d) 19
  27. 27.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  28. 28.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 486 (c) 622 (d) 621
  29. 29.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 16 (c) 51 (d) 48
  30. 30.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 120 (c) 110 (d) 119
  31. 31.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 462 (c) 380 (d) 463
  32. 32.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  33. 33.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 302 (c) 346 (d) 345
  34. 34.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 129 (c) 138 (d) 120
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 15 (b) 17 (c) 9 (d) 18
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 14 (b) 16 (c) 15 (d) 4
  37. 37.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) 117 (b) 13 (c) 39 (d) 42
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 6 (b) 9 (c) 8 (d) 7
  39. 39.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
  40. 40.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5

Answer key

  1. 157
  2. 18
  3. 17
  4. 279
  5. 24
  6. 57
  7. 105
  8. 8
  9. 85
  10. 6
  11. 18
  12. 339
  13. 480
  14. 63
  15. 19
  16. 14
  17. 153
  18. 16
  19. 42
  20. 45
  21. 17
  22. 2
  23. 8
  24. 5
  25. 3
  26. 18
  27. 3
  28. 621
  29. 48
  30. 119
  31. 462
  32. 4
  33. 345
  34. 129
  35. 17
  36. 15
  37. 39
  38. 8
  39. 6
  40. 5

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