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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 778 · 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.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) 36 (b) 33 (c) 99 (d) 11
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 17 (b) 19 (c) 8 (d) 18
  3. 3.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 104 (c) 114 (d) 113
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 3 (b) 5 (c) 6 (d) 4
  6. 6.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 152 (c) 144 (d) 143
  7. 7.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  8. 8.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) 171 (b) 60 (c) 57 (d) 19
  9. 9.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 82? (a) 8 (b) 7 (c) 6 (d) 9
  11. 11.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) 39 (b) 117 (c) 42 (d) 13
  12. 12.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 54 (c) 72 (d) 63
  13. 13.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 26 (b) 35 (c) 36 (d) 44
  14. 14.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  15. 15.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 107 (c) 98 (d) 108
  16. 16.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) 48 (b) 15 (c) 135 (d) 45
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 20 (b) 9 (c) 19 (d) 21
  18. 18.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  19. 19.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 297 (c) 288 (d) 298
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 3 (b) 6 (c) 5 (d) 4
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 12 (b) 13 (c) 3 (d) 14
  22. 22.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 300 (c) 272 (d) 291
  23. 23.The numbers 18 to 26 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) 69 (c) 22 (d) 198
  24. 24.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 541 (c) 540 (d) 432
  25. 25.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
  26. 26.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 262 (c) 246 (d) 252
  27. 27.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 375 (b) 376 (c) 322 (d) 366
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 19 (b) 7 (c) 17 (d) 18
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  30. 30.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) 66 (c) 189 (d) 63
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 2 (b) 5 (c) 4 (d) 3
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 5 (b) 6 (c) 3 (d) 4
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 5 (b) 3 (c) 2 (d) 4
  34. 34.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 282 (c) 315 (d) 316
  35. 35.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) 153 (c) 17 (d) 51
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 1 (b) 4 (c) 3 (d) 2
  37. 37.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) 23 (c) 72 (d) 207
  38. 38.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) 216 (b) 75 (c) 24 (d) 72
  39. 39.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 600 (c) 478 (d) 610
  40. 40.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 116 (c) 115 (d) 124

Answer key

  1. 33
  2. 18
  3. 113
  4. 2
  5. 5
  6. 143
  7. 8
  8. 57
  9. 6
  10. 8
  11. 39
  12. 63
  13. 35
  14. 4
  15. 107
  16. 45
  17. 20
  18. 3
  19. 297
  20. 5
  21. 13
  22. 300
  23. 66
  24. 540
  25. 6
  26. 261
  27. 375
  28. 18
  29. 9
  30. 63
  31. 4
  32. 5
  33. 4
  34. 315
  35. 51
  36. 3
  37. 69
  38. 72
  39. 609
  40. 115

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