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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 503 · 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 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 139 (c) 148 (d) 130
  2. 2.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 37 (b) 46 (c) 28 (d) 38
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 4 (b) 6 (c) 5 (d) 7
  4. 4.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) 144 (c) 153 (d) 154
  5. 5.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 182 (c) 174 (d) 173
  6. 6.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) 51 (c) 16 (d) 48
  7. 7.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 106 (c) 124 (d) 115
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 4 (b) 7 (c) 5 (d) 6
  9. 9.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 13 (d) 6
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 12 (b) 10 (c) 11 (d) 3
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 8 (b) 17 (c) 19 (d) 18
  12. 12.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) 76 (d) 66
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  14. 14.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) 396 (c) 336 (d) 387
  15. 15.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
  16. 16.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  17. 17.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  18. 18.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  19. 19.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) 27 (b) 81 (c) 9 (d) 30
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 16 (b) 15 (c) 7 (d) 17
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 16 (b) 5 (c) 15 (d) 17
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 71? (a) 7 (b) 5 (c) 6 (d) 8
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  24. 24.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
  26. 26.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) 463 (c) 462 (d) 380
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 11 (b) 13 (c) 5 (d) 12
  28. 28.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
  29. 29.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 303 (c) 313 (d) 312
  30. 30.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  31. 31.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) 63 (c) 21 (d) 189
  32. 32.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
  33. 33.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 230 (b) 238 (c) 237 (d) 228
  34. 34.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) 21 (b) 6 (c) 18 (d) 54
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 15 (b) 16 (c) 5 (d) 17
  36. 36.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 274 (c) 294 (d) 303
  37. 37.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 370 (c) 447 (d) 438
  38. 38.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) 135 (c) 48 (d) 45
  39. 39.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) 45 (d) 42
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 13 (b) 10 (c) 12 (d) 9

Answer key

  1. 139
  2. 37
  3. 6
  4. 153
  5. 173
  6. 48
  7. 115
  8. 6
  9. 7
  10. 11
  11. 18
  12. 75
  13. 4
  14. 396
  15. 21
  16. 7
  17. 6
  18. 9
  19. 27
  20. 16
  21. 16
  22. 7
  23. 3
  24. 8
  25. 2
  26. 462
  27. 12
  28. 39
  29. 312
  30. 2
  31. 63
  32. 5
  33. 237
  34. 18
  35. 16
  36. 303
  37. 447
  38. 45
  39. 42
  40. 12

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