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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 579 · 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 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 562 (c) 552 (d) 446
  2. 2.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) 66 (b) 21 (c) 63 (d) 189
  3. 3.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 628 (c) 490 (d) 627
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  5. 5.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 306 (c) 342 (d) 352
  6. 6.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
  7. 7.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) 423 (d) 354
  8. 8.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 625 (c) 488 (d) 624
  9. 9.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 19 (b) 8 (c) 18 (d) 20
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 17 (b) 8 (c) 18 (d) 19
  12. 12.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 170 (c) 179 (d) 180
  13. 13.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 6 (b) 5 (c) 4 (d) 3
  15. 15.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) 216 (d) 75
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 15 (b) 9 (c) 18 (d) 17
  17. 17.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 6 (b) 16 (c) 17 (d) 18
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 54? (a) 17 (b) 16 (c) 5 (d) 15
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 5 (b) 17 (c) 15 (d) 16
  21. 21.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 57? (a) 5 (b) 14 (c) 15 (d) 13
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 20 (b) 19 (c) 21 (d) 9
  24. 24.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  25. 25.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
  26. 26.The numbers 16 to 24 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) 180 (c) 20 (d) 63
  27. 27.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 513 (c) 504 (d) 514
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 4 (d) 3
  29. 29.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 495 (c) 505 (d) 504
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 5 (b) 12 (c) 13 (d) 14
  31. 31.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
  32. 32.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) 30 (b) 27 (c) 9 (d) 81
  33. 33.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 386 (c) 471 (d) 472
  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) 316 (b) 315 (c) 282 (d) 306
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 19 (b) 17 (c) 18 (d) 7
  37. 37.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 37 (b) 28 (c) 46 (d) 38
  38. 38.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
  39. 39.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 288 (c) 289 (d) 279
  40. 40.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) 198 (b) 69 (c) 66 (d) 22

Answer key

  1. 561
  2. 63
  3. 627
  4. 5
  5. 351
  6. 6
  7. 423
  8. 624
  9. 3
  10. 19
  11. 18
  12. 179
  13. 2
  14. 5
  15. 72
  16. 17
  17. 8
  18. 17
  19. 16
  20. 16
  21. 9
  22. 14
  23. 20
  24. 2
  25. 8
  26. 60
  27. 513
  28. 4
  29. 504
  30. 13
  31. 39
  32. 27
  33. 471
  34. 315
  35. 4
  36. 18
  37. 37
  38. 24
  39. 288
  40. 66

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