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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 767 · 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 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 118 (c) 109 (d) 100
  2. 2.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) 171 (b) 19 (c) 57 (d) 60
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 5 (b) 3 (c) 2 (d) 4
  4. 4.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) 14 (b) 42 (c) 126 (d) 45
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 64? (a) 5 (b) 6 (c) 4 (d) 7
  6. 6.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 79 (c) 88 (d) 80
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 1 (b) 2 (c) 3 (d) 4
  8. 8.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
  9. 9.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 7 (d) 6
  10. 10.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) 17 (b) 51 (c) 54 (d) 153
  11. 11.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) 42 (b) 117 (c) 13 (d) 39
  12. 12.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) 81 (b) 27 (c) 30 (d) 9
  13. 13.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  14. 14.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) 108 (b) 39 (c) 12 (d) 36
  15. 15.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) 21 (b) 24 (c) 63 (d) 7
  16. 16.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 207 (c) 210 (d) 198
  17. 17.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 589 (b) 464 (c) 579 (d) 588
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 6 (b) 3 (c) 5 (d) 4
  19. 19.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 204 (c) 205 (d) 208
  20. 20.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 66 (c) 57 (d) 48
  21. 21.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) 60 (b) 63 (c) 180 (d) 20
  22. 22.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 325 (c) 315 (d) 324
  23. 23.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 256 (c) 242 (d) 255
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  25. 25.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 63 (c) 54 (d) 64
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 3 (b) 14 (c) 15 (d) 13
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 19 (b) 17 (c) 18 (d) 7
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 9 (b) 20 (c) 21 (d) 19
  29. 29.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) 99 (b) 11 (c) 33 (d) 36
  30. 30.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) 10 (c) 30 (d) 90
  31. 31.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 52 (c) 62 (d) 61
  32. 32.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 586 (c) 462 (d) 585
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 10 (b) 5 (c) 11 (d) 8
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 18 (b) 6 (c) 16 (d) 17
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 50? (a) 4 (b) 6 (c) 5 (d) 3
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 58? (a) 17 (b) 15 (c) 5 (d) 16
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 17 (b) 19 (c) 18 (d) 8
  38. 38.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 577 (c) 567 (d) 456
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 16 (d) 15
  40. 40.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 142 (c) 133 (d) 134

Answer key

  1. 109
  2. 57
  3. 4
  4. 42
  5. 6
  6. 79
  7. 3
  8. 7
  9. 6
  10. 51
  11. 39
  12. 27
  13. 4
  14. 36
  15. 21
  16. 207
  17. 588
  18. 5
  19. 204
  20. 57
  21. 60
  22. 324
  23. 255
  24. 3
  25. 63
  26. 14
  27. 18
  28. 20
  29. 33
  30. 30
  31. 61
  32. 585
  33. 10
  34. 17
  35. 5
  36. 16
  37. 18
  38. 576
  39. 16
  40. 133

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