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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 303 · 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 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 456 (c) 567 (d) 576
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 17 (b) 19 (c) 7 (d) 18
  3. 3.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 404 (c) 499 (d) 498
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 5 (b) 14 (c) 13 (d) 12
  5. 5.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 6 (d) 14
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 19 (b) 18 (c) 8 (d) 17
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 1 (b) 4 (c) 2 (d) 3
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 14 (b) 13 (c) 4 (d) 15
  9. 9.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 414 (c) 354 (d) 423
  10. 10.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 232 (c) 241 (d) 240
  11. 11.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) 24 (d) 27
  12. 12.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
  13. 13.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 161 (b) 152 (c) 170 (d) 162
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 18 (b) 20 (c) 8 (d) 19
  15. 15.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 211 (b) 210 (c) 212 (d) 201
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 18 (b) 20 (c) 8 (d) 19
  17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 5 (b) 4 (c) 6 (d) 3
  18. 18.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 361 (c) 360 (d) 312
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 1 (b) 4 (c) 3 (d) 2
  20. 20.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 483 (c) 474 (d) 484
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 5 (b) 8 (c) 6 (d) 7
  22. 22.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 72 (c) 62 (d) 71
  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) 22 (b) 69 (c) 66 (d) 198
  24. 24.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 8 (b) 19 (c) 17 (d) 18
  26. 26.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 10 (d) 7
  27. 27.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 367 (b) 316 (c) 357 (d) 366
  28. 28.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 132 (c) 141 (d) 142
  29. 29.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18
  31. 31.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 222 (c) 213 (d) 223
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 16 (b) 15 (c) 17 (d) 5
  33. 33.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 9 (d) 10
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 73? (a) 18 (b) 7 (c) 16 (d) 17
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 6 (b) 7 (c) 5 (d) 8
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 14 (b) 15 (c) 4 (d) 16
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 10 (b) 7 (c) 13 (d) 12
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 18 (b) 16 (c) 17 (d) 6
  39. 39.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 410 (b) 508 (c) 498 (d) 507
  40. 40.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8

Answer key

  1. 576
  2. 18
  3. 498
  4. 13
  5. 6
  6. 18
  7. 3
  8. 14
  9. 423
  10. 240
  11. 24
  12. 39
  13. 161
  14. 19
  15. 210
  16. 19
  17. 5
  18. 360
  19. 3
  20. 483
  21. 7
  22. 71
  23. 66
  24. 2
  25. 18
  26. 6
  27. 366
  28. 141
  29. 2
  30. 19
  31. 222
  32. 16
  33. 8
  34. 17
  35. 7
  36. 15
  37. 12
  38. 17
  39. 507
  40. 7

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