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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 533 · 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 62? (a) 5 (b) 4 (c) 7 (d) 6
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 16 (b) 4 (c) 14 (d) 15
  3. 3.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 600 (c) 601 (d) 472
  4. 4.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
  5. 5.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 3 (d) 16
  6. 6.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 15 (b) 14 (c) 3 (d) 13
  8. 8.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 250 (c) 249 (d) 238
  9. 9.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 213 (c) 223 (d) 220
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 19 (b) 17 (c) 7 (d) 18
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 3 (b) 14 (c) 13 (d) 15
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 6 (b) 17 (c) 18 (d) 16
  13. 13.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 2 (b) 3 (c) 5 (d) 4
  15. 15.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 295 (c) 268 (d) 294
  16. 16.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) 57 (b) 18 (c) 54 (d) 162
  17. 17.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 136 (c) 145 (d) 154
  18. 18.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 416 (b) 507 (c) 517 (d) 516
  19. 19.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) 21 (c) 63 (d) 66
  20. 20.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 68 (c) 60 (d) 59
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 6 (b) 16 (c) 15 (d) 17
  22. 22.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
  23. 23.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 116 (c) 98 (d) 107
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 18 (b) 20 (c) 8 (d) 19
  25. 25.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) 117 (b) 42 (c) 39 (d) 13
  26. 26.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) 63 (b) 180 (c) 60 (d) 20
  27. 27.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) 54 (c) 153 (d) 51
  28. 28.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 595 (c) 585 (d) 594
  29. 29.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) 69 (b) 207 (c) 72 (d) 23
  30. 30.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) 36 (b) 99 (c) 33 (d) 11
  31. 31.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) 39 (b) 36 (c) 108 (d) 12
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 32? (a) 4 (b) 2 (c) 3 (d) 1
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 16 (b) 4 (c) 15 (d) 14
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 7 (b) 3 (c) 8 (d) 9
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 14 (b) 3 (c) 13 (d) 15
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 4 (d) 1
  37. 37.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  38. 38.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
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 45? (a) 3 (b) 5 (c) 2 (d) 4
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 96? (a) 17 (b) 14 (c) 9 (d) 16

Answer key

  1. 6
  2. 15
  3. 600
  4. 8
  5. 4
  6. 8
  7. 14
  8. 249
  9. 222
  10. 18
  11. 14
  12. 17
  13. 5
  14. 4
  15. 294
  16. 54
  17. 145
  18. 516
  19. 63
  20. 59
  21. 16
  22. 3
  23. 107
  24. 19
  25. 39
  26. 60
  27. 51
  28. 594
  29. 69
  30. 33
  31. 36
  32. 3
  33. 15
  34. 8
  35. 14
  36. 3
  37. 2
  38. 72
  39. 4
  40. 16

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