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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 771 · 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 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 616 (b) 606 (c) 482 (d) 615
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  3. 3.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 68 (c) 50 (d) 59
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 17 (b) 7 (c) 19 (d) 18
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 4 (b) 6 (c) 7 (d) 5
  6. 6.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 320 (c) 363 (d) 373
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 71? (a) 7 (b) 6 (c) 8 (d) 5
  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) 45 (b) 15 (c) 18 (d) 5
  9. 9.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 390 (c) 399 (d) 338
  10. 10.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  11. 11.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  12. 12.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 8 (d) 10
  13. 13.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) 189 (b) 66 (c) 21 (d) 63
  14. 14.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 117 (c) 118 (d) 126
  15. 15.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) 148 (c) 166 (d) 158
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 2 (d) 17
  17. 17.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
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 17 (b) 18 (c) 19 (d) 8
  19. 19.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 90 (c) 89 (d) 80
  20. 20.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 352 (c) 420 (d) 421
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 1 (b) 4 (c) 2 (d) 3
  22. 22.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 144 (c) 162 (d) 153
  23. 23.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) 6 (b) 18 (c) 54 (d) 21
  24. 24.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 119 (b) 120 (c) 128 (d) 110
  25. 25.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 7 (d) 6
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 9 (b) 20 (c) 21 (d) 19
  27. 27.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 394 (c) 483 (d) 474
  28. 28.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  29. 29.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 517 (b) 516 (c) 507 (d) 416
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 3 (b) 4 (c) 1 (d) 2
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 6 (b) 18 (c) 17 (d) 16
  32. 32.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 278 (b) 310 (c) 309 (d) 300
  33. 33.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) 27 (c) 72 (d) 8
  34. 34.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 298 (c) 270 (d) 288
  35. 35.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 10 (d) 9
  36. 36.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 146 (c) 156 (d) 155
  37. 37.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 5 (b) 4 (c) 3 (d) 2
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 19 (b) 17 (c) 8 (d) 18
  40. 40.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) 42 (d) 39

Answer key

  1. 615
  2. 9
  3. 59
  4. 18
  5. 6
  6. 372
  7. 7
  8. 15
  9. 399
  10. 6
  11. 5
  12. 7
  13. 63
  14. 117
  15. 157
  16. 3
  17. 51
  18. 18
  19. 89
  20. 420
  21. 3
  22. 153
  23. 18
  24. 119
  25. 6
  26. 20
  27. 483
  28. 7
  29. 516
  30. 3
  31. 17
  32. 309
  33. 24
  34. 297
  35. 9
  36. 155
  37. 4
  38. 4
  39. 18
  40. 39

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