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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 18 · 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 12? (a) 8 (b) 13 (c) 6 (d) 7
  2. 2.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 6 (b) 18 (c) 16 (d) 17
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 5 (b) 3 (c) 4 (d) 2
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 6 (b) 16 (c) 17 (d) 18
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 19 (b) 20 (c) 18 (d) 8
  7. 7.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 604 (b) 594 (c) 603 (d) 474
  8. 8.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) 168 (c) 158 (d) 167
  9. 9.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 3 (b) 15 (c) 14 (d) 13
  11. 11.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 31 (b) 32 (c) 22 (d) 40
  12. 12.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
  13. 13.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) 36 (b) 12 (c) 39 (d) 108
  14. 14.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 158 (c) 157 (d) 166
  15. 15.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  16. 16.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
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 5 (b) 4 (c) 6 (d) 7
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 18 (d) 20
  19. 19.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 5 (b) 15 (c) 16 (d) 17
  21. 21.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) 21 (b) 6 (c) 18 (d) 54
  22. 22.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4
  23. 23.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) 20 (d) 180
  24. 24.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) 69 (c) 23 (d) 207
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 8 (b) 7 (c) 9 (d) 6
  26. 26.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 5 (b) 4 (c) 6 (d) 3
  28. 28.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) 45 (b) 48 (c) 135 (d) 15
  29. 29.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 165 (b) 156 (c) 166 (d) 174
  30. 30.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 320 (b) 373 (c) 372 (d) 363
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 12 (b) 14 (c) 13 (d) 3
  32. 32.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 141 (c) 132 (d) 142
  33. 33.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) 90 (b) 10 (c) 33 (d) 30
  34. 34.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 457 (b) 447 (c) 456 (d) 376
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 5 (b) 4 (c) 3 (d) 6
  36. 36.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 594 (c) 468 (d) 595
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 6 (b) 18 (c) 16 (d) 17
  38. 38.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 143 (c) 152 (d) 144
  39. 39.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) 153 (c) 51 (d) 54
  40. 40.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 429 (c) 358 (d) 430

Answer key

  1. 7
  2. 9
  3. 17
  4. 4
  5. 17
  6. 19
  7. 603
  8. 167
  9. 8
  10. 14
  11. 31
  12. 72
  13. 36
  14. 157
  15. 6
  16. 63
  17. 6
  18. 19
  19. 8
  20. 16
  21. 18
  22. 4
  23. 60
  24. 69
  25. 8
  26. 5
  27. 5
  28. 45
  29. 165
  30. 372
  31. 13
  32. 141
  33. 30
  34. 456
  35. 5
  36. 594
  37. 17
  38. 143
  39. 51
  40. 429

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