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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 438 · 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 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 406 (c) 501 (d) 502
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 14 (b) 5 (c) 13 (d) 12
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 4 (b) 7 (c) 6 (d) 5
  4. 4.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
  5. 5.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 342 (c) 396 (d) 406
  6. 6.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 168 (c) 159 (d) 150
  7. 7.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  8. 8.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) 5 (b) 45 (c) 18 (d) 15
  9. 9.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 222 (c) 231 (d) 232
  10. 10.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 4 (d) 17
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 5 (b) 8 (c) 7 (d) 6
  12. 12.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) 24 (b) 8 (c) 27 (d) 72
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 5 (b) 3 (c) 2 (d) 4
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 2 (b) 3 (c) 4 (d) 1
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 19 (b) 18 (c) 8 (d) 17
  16. 16.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) 51 (b) 54 (c) 153 (d) 17
  17. 17.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  18. 18.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
  19. 19.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 165 (b) 166 (c) 174 (d) 156
  20. 20.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 6 (d) 14
  21. 21.The numbers 8 to 16 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) 36 (c) 12 (d) 108
  22. 22.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 351 (c) 243 (d) 234
  23. 23.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) 57 (b) 171 (c) 60 (d) 19
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 13 (b) 14 (c) 15 (d) 3
  25. 25.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) 23 (b) 72 (c) 207 (d) 69
  26. 26.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 54 (c) 162 (d) 18
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 4 (b) 5 (c) 3 (d) 2
  28. 28.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 155 (b) 164 (c) 146 (d) 156
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 7 (b) 6 (c) 4 (d) 5
  30. 30.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 330 (c) 387 (d) 378
  31. 31.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 325 (b) 324 (c) 315 (d) 288
  32. 32.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) 7 (c) 63 (d) 21
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 21 (b) 9 (c) 20 (d) 19
  34. 34.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 1 (b) 2 (c) 3 (d) 4
  36. 36.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  37. 37.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  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) 72 (b) 24 (c) 75 (d) 216
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 10 (b) 11 (c) 9 (d) 4
  40. 40.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10

Answer key

  1. 501
  2. 13
  3. 6
  4. 9
  5. 405
  6. 159
  7. 2
  8. 15
  9. 231
  10. 3
  11. 7
  12. 24
  13. 4
  14. 3
  15. 18
  16. 51
  17. 5
  18. 113
  19. 165
  20. 6
  21. 36
  22. 243
  23. 57
  24. 14
  25. 69
  26. 54
  27. 4
  28. 155
  29. 6
  30. 387
  31. 324
  32. 21
  33. 20
  34. 6
  35. 3
  36. 2
  37. 4
  38. 72
  39. 10
  40. 7

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