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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 848 · 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 2 written when you write all the numbers from 1 to 90? (a) 20 (b) 9 (c) 18 (d) 19
  2. 2.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) 167 (c) 158 (d) 168
  3. 3.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 445 (b) 435 (c) 444 (d) 368
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 15 (b) 13 (c) 3 (d) 14
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 3 (b) 2 (c) 4 (d) 5
  6. 6.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 474 (c) 465 (d) 475
  7. 7.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  8. 8.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) 144 (b) 51 (c) 16 (d) 48
  9. 9.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) 162 (b) 54 (c) 18 (d) 57
  10. 10.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  11. 11.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 95? (a) 18 (b) 9 (c) 20 (d) 19
  13. 13.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 147 (c) 148 (d) 138
  14. 14.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) 594 (c) 595 (d) 585
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 2 (b) 3 (c) 4 (d) 5
  16. 16.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) 36 (d) 12
  17. 17.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) 30 (c) 9 (d) 27
  18. 18.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) 45 (c) 48 (d) 135
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 4 (b) 2 (c) 3 (d) 5
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 17 (b) 5 (c) 16 (d) 15
  22. 22.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 616 (c) 606 (d) 482
  23. 23.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) 54 (b) 17 (c) 51 (d) 153
  24. 24.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) 10 (b) 90 (c) 33 (d) 30
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 9 (b) 6 (c) 7 (d) 8
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 4 (b) 2 (c) 3 (d) 1
  27. 27.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 519 (b) 529 (c) 528 (d) 424
  28. 28.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 272 (c) 300 (d) 291
  29. 29.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 207 (c) 210 (d) 208
  30. 30.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 148 (c) 158 (d) 157
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 16 (b) 18 (c) 17 (d) 6
  32. 32.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) 69 (b) 22 (c) 66 (d) 198
  33. 33.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 5 (b) 16 (c) 14 (d) 15
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 6 (b) 3 (c) 5 (d) 4
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 9 (b) 18 (c) 19 (d) 20
  37. 37.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  38. 38.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  39. 39.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) 72 (d) 75
  40. 40.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2

Answer key

  1. 19
  2. 167
  3. 444
  4. 14
  5. 4
  6. 474
  7. 3
  8. 48
  9. 54
  10. 5
  11. 6
  12. 19
  13. 147
  14. 594
  15. 4
  16. 36
  17. 27
  18. 45
  19. 4
  20. 3
  21. 16
  22. 615
  23. 51
  24. 30
  25. 8
  26. 3
  27. 528
  28. 300
  29. 207
  30. 157
  31. 17
  32. 66
  33. 2
  34. 15
  35. 5
  36. 19
  37. 7
  38. 6
  39. 72
  40. 2

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