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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 860 · 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.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 14 (b) 15 (c) 13 (d) 3
  2. 2.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 154 (c) 153 (d) 144
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 14 (b) 11 (c) 8 (d) 13
  4. 4.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 327 (c) 337 (d) 336
  5. 5.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) 20 (b) 60 (c) 63 (d) 180
  6. 6.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 26 (c) 36 (d) 35
  7. 7.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 52 (c) 60 (d) 51
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 7 (b) 19 (c) 17 (d) 18
  9. 9.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5
  10. 10.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) 63 (b) 21 (c) 66 (d) 189
  11. 11.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  12. 12.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 162 (b) 57 (c) 54 (d) 18
  13. 13.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 456 (c) 577 (d) 576
  14. 14.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) 75 (c) 24 (d) 216
  15. 15.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) 69 (d) 198
  16. 16.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  17. 17.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) 643 (d) 642
  18. 18.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) 54 (b) 21 (c) 6 (d) 18
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 17 (b) 16 (c) 6 (d) 18
  20. 20.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 298 (c) 297 (d) 270
  21. 21.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 482 (b) 616 (c) 606 (d) 615
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 95? (a) 18 (b) 19 (c) 9 (d) 20
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 3 (b) 2 (c) 4 (d) 1
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 15 (b) 17 (c) 16 (d) 6
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 93? (a) 18 (b) 20 (c) 19 (d) 9
  26. 26.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) 30 (b) 90 (c) 33 (d) 10
  27. 27.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 120 (c) 111 (d) 102
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 6 (b) 5 (c) 3 (d) 4
  29. 29.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 44? (a) 2 (b) 3 (c) 5 (d) 4
  31. 31.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  32. 32.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 556 (c) 442 (d) 555
  33. 33.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) 153 (b) 17 (c) 51 (d) 54
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 16 (b) 7 (c) 17 (d) 18
  35. 35.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 39 (b) 48 (c) 40 (d) 30
  36. 36.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
  37. 37.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  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) 24 (b) 7 (c) 21 (d) 63
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 14 (b) 15 (c) 16 (d) 4
  40. 40.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 272 (c) 291 (d) 301

Answer key

  1. 14
  2. 153
  3. 13
  4. 336
  5. 60
  6. 35
  7. 51
  8. 18
  9. 6
  10. 63
  11. 4
  12. 54
  13. 576
  14. 72
  15. 66
  16. 5
  17. 642
  18. 18
  19. 17
  20. 297
  21. 615
  22. 19
  23. 3
  24. 16
  25. 19
  26. 30
  27. 111
  28. 5
  29. 5
  30. 4
  31. 7
  32. 555
  33. 51
  34. 17
  35. 39
  36. 2
  37. 3
  38. 21
  39. 15
  40. 300

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