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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 257 · 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 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 387 (c) 330 (d) 378
  2. 2.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 538 (b) 528 (c) 537 (d) 430
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  4. 4.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 321 (c) 286 (d) 322
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 3 (b) 2 (c) 5 (d) 4
  6. 6.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  7. 7.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 14 (b) 15 (c) 3 (d) 13
  10. 10.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 121 (b) 112 (c) 130 (d) 122
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 15 (b) 14 (c) 13 (d) 3
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 8 (b) 17 (c) 18 (d) 19
  13. 13.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) 15 (b) 45 (c) 5 (d) 18
  14. 14.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  15. 15.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) 63 (d) 21
  16. 16.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 382 (c) 381 (d) 326
  17. 17.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 126 (c) 136 (d) 135
  18. 18.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 21 (b) 20 (c) 9 (d) 19
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 16 (b) 5 (c) 15 (d) 17
  21. 21.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 6 (b) 3 (c) 4 (d) 5
  23. 23.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 108 (c) 39 (d) 12
  24. 24.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) 33 (b) 90 (c) 30 (d) 10
  25. 25.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) 54 (b) 18 (c) 57 (d) 162
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 7 (b) 3 (c) 4 (d) 6
  27. 27.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) 24 (b) 216 (c) 75 (d) 72
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 45? (a) 2 (b) 3 (c) 5 (d) 4
  29. 29.The numbers 12 to 20 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) 48 (c) 144 (d) 16
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 88? (a) 8 (b) 18 (c) 19 (d) 20
  31. 31.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 124 (c) 132 (d) 123
  32. 32.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 67 (c) 68 (d) 76
  33. 33.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 260 (b) 273 (c) 283 (d) 282
  34. 34.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 424 (c) 423 (d) 354
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 6 (b) 5 (c) 7 (d) 8
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 73? (a) 18 (b) 16 (c) 7 (d) 17
  37. 37.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) 42 (c) 126 (d) 14
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 17 (b) 7 (c) 16 (d) 15
  39. 39.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) 21 (c) 18 (d) 54
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 21 (b) 19 (c) 9 (d) 20

Answer key

  1. 387
  2. 537
  3. 5
  4. 321
  5. 4
  6. 7
  7. 5
  8. 9
  9. 14
  10. 121
  11. 14
  12. 18
  13. 15
  14. 4
  15. 63
  16. 381
  17. 135
  18. 3
  19. 20
  20. 16
  21. 8
  22. 5
  23. 36
  24. 30
  25. 54
  26. 6
  27. 72
  28. 4
  29. 48
  30. 19
  31. 123
  32. 67
  33. 282
  34. 423
  35. 7
  36. 17
  37. 42
  38. 16
  39. 18
  40. 20

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