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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 626 · 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 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 222 (c) 223 (d) 213
  2. 2.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 410 (c) 507 (d) 508
  3. 3.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) 24 (c) 27 (d) 72
  4. 4.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 260 (c) 283 (d) 282
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 4 (b) 5 (c) 3 (d) 2
  6. 6.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 559 (b) 549 (c) 444 (d) 558
  7. 7.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  8. 8.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  9. 9.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) 288 (d) 315
  10. 10.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  11. 11.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  12. 12.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 580 (b) 458 (c) 579 (d) 570
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 9 (d) 19
  14. 14.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) 19 (b) 171 (c) 60 (d) 57
  15. 15.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  16. 16.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 600 (b) 478 (c) 610 (d) 609
  17. 17.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) 24 (c) 7 (d) 21
  18. 18.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 642 (b) 643 (c) 500 (d) 633
  19. 19.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 135 (c) 126 (d) 144
  20. 20.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 33 (c) 10 (d) 30
  21. 21.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) 216 (b) 72 (c) 24 (d) 75
  22. 22.The numbers 10 to 18 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) 126 (c) 14 (d) 42
  23. 23.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) 514 (c) 513 (d) 504
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 16 (b) 17 (c) 18 (d) 7
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 1 (d) 3
  26. 26.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4
  27. 27.The numbers 11 to 19 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) 48 (c) 135 (d) 15
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 13 (b) 14 (c) 15 (d) 3
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 20 (b) 9 (c) 21 (d) 19
  30. 30.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
  31. 31.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 6 (b) 3 (c) 4 (d) 5
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 6 (b) 5 (c) 7 (d) 4
  34. 34.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 9 (b) 21 (c) 20 (d) 19
  36. 36.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  37. 37.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 385 (b) 375 (c) 328 (d) 384
  38. 38.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 1 (b) 3 (c) 4 (d) 2
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 17 (b) 8 (c) 19 (d) 18

Answer key

  1. 222
  2. 507
  3. 24
  4. 282
  5. 4
  6. 558
  7. 7
  8. 3
  9. 324
  10. 9
  11. 8
  12. 579
  13. 19
  14. 57
  15. 4
  16. 609
  17. 21
  18. 642
  19. 135
  20. 30
  21. 72
  22. 42
  23. 513
  24. 17
  25. 3
  26. 4
  27. 45
  28. 14
  29. 20
  30. 37
  31. 5
  32. 5
  33. 6
  34. 2
  35. 20
  36. 9
  37. 384
  38. 2
  39. 3
  40. 18

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