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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 210 · 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 1 written when you write all the numbers from 1 to 30? (a) 13 (b) 12 (c) 3 (d) 14
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 20 (b) 9 (c) 19 (d) 21
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 18 (b) 17 (c) 19 (d) 8
  4. 4.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  5. 5.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 8 (b) 19 (c) 17 (d) 18
  7. 7.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 607 (c) 476 (d) 606
  8. 8.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) 12 (b) 39 (c) 36 (d) 108
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 81? (a) 8 (b) 17 (c) 19 (d) 18
  10. 10.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) 8 (c) 27 (d) 24
  11. 11.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 147 (c) 156 (d) 138
  12. 12.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 201 (c) 211 (d) 212
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 4 (b) 16 (c) 14 (d) 15
  14. 14.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) 33 (c) 11 (d) 36
  15. 15.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 166 (c) 156 (d) 165
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 7 (b) 5 (c) 6 (d) 4
  17. 17.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 150 (c) 160 (d) 159
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 8 (b) 5 (c) 7 (d) 4
  19. 19.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
  20. 20.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 3 (b) 2 (c) 4 (d) 5
  22. 22.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 41 (c) 42 (d) 50
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 2 (b) 5 (c) 4 (d) 3
  24. 24.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  25. 25.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  26. 26.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  27. 27.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  28. 28.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 16 (b) 51 (c) 144 (d) 48
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 5 (b) 15 (c) 17 (d) 16
  30. 30.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) 9 (c) 30 (d) 27
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 18 (b) 17 (c) 7 (d) 16
  32. 32.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 184 (c) 183 (d) 174
  33. 33.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 374 (b) 454 (c) 444 (d) 453
  34. 34.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) 20 (b) 60 (c) 180 (d) 63
  35. 35.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 198 (b) 69 (c) 22 (d) 66
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 9 (b) 20 (c) 19 (d) 18
  37. 37.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
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 8 (b) 19 (c) 20 (d) 18
  39. 39.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 282 (c) 291 (d) 266
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 2 (b) 3 (c) 5 (d) 4

Answer key

  1. 13
  2. 20
  3. 18
  4. 2
  5. 5
  6. 18
  7. 606
  8. 36
  9. 18
  10. 24
  11. 147
  12. 210
  13. 15
  14. 33
  15. 165
  16. 6
  17. 159
  18. 7
  19. 9
  20. 2
  21. 4
  22. 41
  23. 4
  24. 6
  25. 6
  26. 7
  27. 3
  28. 48
  29. 16
  30. 27
  31. 17
  32. 183
  33. 453
  34. 60
  35. 66
  36. 19
  37. 603
  38. 19
  39. 291
  40. 4

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