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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 588 · 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 7 written when you write all the numbers from 1 to 90? (a) 9 (b) 20 (c) 18 (d) 19
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  3. 3.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 375 (c) 328 (d) 385
  4. 4.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  5. 5.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
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 20 (b) 19 (c) 21 (d) 9
  7. 7.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) 9 (b) 81 (c) 27 (d) 30
  8. 8.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) 198 (d) 66
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 91? (a) 20 (b) 19 (c) 18 (d) 9
  10. 10.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
  11. 11.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 23 (c) 72 (d) 69
  12. 12.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) 18 (b) 15 (c) 45 (d) 5
  13. 13.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  14. 14.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 20 (b) 21 (c) 19 (d) 9
  16. 16.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 62 (c) 71 (d) 80
  17. 17.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) 498 (c) 404 (d) 499
  18. 18.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 487 (c) 477 (d) 396
  19. 19.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 555 (c) 546 (d) 556
  20. 20.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  21. 21.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
  22. 22.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) 13 (b) 117 (c) 42 (d) 39
  23. 23.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 17 (b) 16 (c) 5 (d) 15
  25. 25.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 141 (b) 142 (c) 132 (d) 150
  26. 26.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 9 (b) 8 (c) 6 (d) 7
  28. 28.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 105 (c) 106 (d) 114
  29. 29.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 56 (c) 47 (d) 38
  30. 30.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 100 (c) 109 (d) 110
  31. 31.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) 33 (c) 90 (d) 10
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 19 (b) 17 (c) 7 (d) 18
  33. 33.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
  34. 34.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 386 (b) 462 (c) 472 (d) 471
  35. 35.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) 18 (b) 162 (c) 57 (d) 54
  36. 36.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 80? (a) 10 (b) 7 (c) 8 (d) 9
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 19 (d) 7
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 15 (b) 13 (c) 3 (d) 14
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 19 (b) 8 (c) 20 (d) 18

Answer key

  1. 19
  2. 9
  3. 384
  4. 6
  5. 63
  6. 20
  7. 27
  8. 66
  9. 19
  10. 297
  11. 69
  12. 15
  13. 7
  14. 4
  15. 20
  16. 71
  17. 498
  18. 486
  19. 555
  20. 5
  21. 4
  22. 39
  23. 8
  24. 16
  25. 141
  26. 2
  27. 8
  28. 105
  29. 47
  30. 109
  31. 30
  32. 18
  33. 14
  34. 471
  35. 54
  36. 8
  37. 9
  38. 18
  39. 14
  40. 19

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