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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 193 · 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 two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  2. 2.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) 27 (b) 24 (c) 72 (d) 8
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 8 (b) 6 (c) 9 (d) 4
  4. 4.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) 18 (c) 5 (d) 45
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 3 (d) 4
  6. 6.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 137 (b) 138 (c) 146 (d) 128
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 20 (d) 21
  8. 8.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) 216 (b) 75 (c) 24 (d) 72
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 58? (a) 16 (b) 15 (c) 17 (d) 5
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 19 (d) 18
  11. 11.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 502 (c) 492 (d) 501
  12. 12.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 170 (c) 161 (d) 162
  13. 13.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) 133 (c) 134 (d) 142
  14. 14.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) 63 (c) 7 (d) 24
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 3 (b) 13 (c) 14 (d) 15
  16. 16.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  17. 17.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 411 (c) 402 (d) 412
  18. 18.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  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) 63 (b) 189 (c) 21 (d) 66
  20. 20.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 114 (c) 113 (d) 122
  21. 21.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  22. 22.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) 54 (d) 18
  23. 23.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 561 (c) 571 (d) 452
  24. 24.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 7 (d) 5
  25. 25.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 337 (c) 327 (d) 296
  26. 26.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 324 (c) 379 (d) 369
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 5 (b) 4 (c) 6 (d) 3
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 17 (b) 15 (c) 5 (d) 16
  29. 29.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 68 (c) 50 (d) 59
  30. 30.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 70 (c) 69 (d) 60
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 16 (b) 5 (c) 17 (d) 15
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 5 (b) 7 (c) 6 (d) 8
  33. 33.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) 15 (b) 135 (c) 48 (d) 45
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 18 (b) 9 (c) 20 (d) 19
  35. 35.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 360 (c) 361 (d) 312
  36. 36.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 40? (a) 4 (b) 6 (c) 3 (d) 5
  38. 38.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 94? (a) 9 (b) 12 (c) 15 (d) 14
  40. 40.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) 60 (b) 19 (c) 57 (d) 171

Answer key

  1. 3
  2. 24
  3. 8
  4. 15
  5. 3
  6. 137
  7. 20
  8. 72
  9. 16
  10. 19
  11. 501
  12. 161
  13. 133
  14. 21
  15. 14
  16. 4
  17. 411
  18. 5
  19. 63
  20. 113
  21. 7
  22. 18
  23. 570
  24. 6
  25. 336
  26. 378
  27. 5
  28. 16
  29. 59
  30. 69
  31. 16
  32. 7
  33. 45
  34. 19
  35. 360
  36. 9
  37. 5
  38. 2
  39. 14
  40. 57

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