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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 493 · 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 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 122 (c) 132 (d) 131
  2. 2.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) 174 (c) 156 (d) 166
  3. 3.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 14 (b) 3 (c) 15 (d) 13
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 16 (b) 4 (c) 14 (d) 15
  6. 6.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  7. 7.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 567 (c) 568 (d) 558
  8. 8.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 492 (c) 483 (d) 493
  9. 9.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 154 (c) 172 (d) 163
  10. 10.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) 22 (b) 66 (c) 198 (d) 69
  11. 11.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 30 (b) 48 (c) 39 (d) 40
  12. 12.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 181 (c) 190 (d) 172
  13. 13.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
  14. 14.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
  15. 15.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 92 (c) 102 (d) 101
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 19 (b) 21 (c) 9 (d) 20
  17. 17.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 15 (b) 14 (c) 7 (d) 12
  19. 19.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) 45 (b) 15 (c) 5 (d) 18
  20. 20.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) 18 (c) 54 (d) 6
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 13 (b) 7 (c) 12 (d) 10
  22. 22.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 582 (c) 466 (d) 592
  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) 60 (b) 19 (c) 171 (d) 57
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 4 (b) 3 (c) 2 (d) 1
  25. 25.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  26. 26.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 249 (c) 244 (d) 259
  27. 27.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 97 (c) 88 (d) 106
  28. 28.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 37 (c) 28 (d) 46
  29. 29.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 104 (c) 96 (d) 95
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 4 (b) 2 (c) 3 (d) 5
  31. 31.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) 17 (b) 153 (c) 54 (d) 51
  32. 32.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
  33. 33.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 403 (b) 393 (c) 402 (d) 340
  34. 34.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 100 (c) 92 (d) 91
  35. 35.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) 30 (c) 81 (d) 9
  36. 36.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 500 (c) 642 (d) 643
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 9 (b) 20 (c) 19 (d) 18
  38. 38.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) 63 (b) 7 (c) 24 (d) 21
  39. 39.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 80 (c) 71 (d) 72
  40. 40.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 576 (c) 586 (d) 585

Answer key

  1. 131
  2. 165
  3. 8
  4. 14
  5. 15
  6. 8
  7. 567
  8. 492
  9. 163
  10. 66
  11. 39
  12. 181
  13. 2
  14. 24
  15. 101
  16. 20
  17. 3
  18. 14
  19. 15
  20. 18
  21. 12
  22. 591
  23. 57
  24. 3
  25. 5
  26. 258
  27. 97
  28. 37
  29. 95
  30. 4
  31. 51
  32. 7
  33. 402
  34. 91
  35. 27
  36. 642
  37. 19
  38. 21
  39. 71
  40. 585

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