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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 287 · 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.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) 72 (b) 207 (c) 23 (d) 69
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 1 (b) 4 (c) 2 (d) 3
  3. 3.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  4. 4.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 122 (c) 121 (d) 112
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 9 (b) 21 (c) 20 (d) 19
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 67? (a) 6 (b) 8 (c) 7 (d) 5
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 3 (b) 5 (c) 2 (d) 4
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  9. 9.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) 42 (b) 45 (c) 126 (d) 14
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 15 (b) 14 (c) 12 (d) 7
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 4 (b) 3 (c) 5 (d) 2
  13. 13.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) 72 (b) 27 (c) 8 (d) 24
  14. 14.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) 162 (d) 57
  15. 15.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) 5 (b) 45 (c) 18 (d) 15
  16. 16.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) 75 (d) 216
  17. 17.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 493 (c) 483 (d) 400
  18. 18.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 158 (c) 168 (d) 167
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 1 (b) 4 (c) 2 (d) 3
  20. 20.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  22. 22.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 3 (b) 6 (c) 5 (d) 4
  24. 24.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 331 (c) 292 (d) 321
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 3 (b) 14 (c) 13 (d) 15
  26. 26.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 544 (c) 534 (d) 434
  27. 27.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 586 (b) 585 (c) 462 (d) 576
  28. 28.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 117 (c) 108 (d) 118
  29. 29.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  30. 30.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 435 (c) 368 (d) 445
  31. 31.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 125 (b) 126 (c) 116 (d) 134
  32. 32.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
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 5 (b) 3 (c) 4 (d) 6
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 5 (d) 2
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 18 (b) 8 (c) 19 (d) 20
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 21 (b) 9 (c) 20 (d) 19
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 15 (b) 14 (c) 4 (d) 16
  38. 38.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 33 (c) 99 (d) 36
  39. 39.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) 135 (b) 48 (c) 15 (d) 45
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 18 (b) 19 (c) 20 (d) 9

Answer key

  1. 69
  2. 3
  3. 4
  4. 121
  5. 20
  6. 7
  7. 4
  8. 8
  9. 42
  10. 3
  11. 14
  12. 4
  13. 24
  14. 54
  15. 15
  16. 72
  17. 492
  18. 167
  19. 3
  20. 6
  21. 7
  22. 3
  23. 5
  24. 330
  25. 14
  26. 543
  27. 585
  28. 117
  29. 5
  30. 444
  31. 125
  32. 30
  33. 5
  34. 4
  35. 19
  36. 20
  37. 15
  38. 33
  39. 45
  40. 19

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