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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 751 · 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.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) 45 (d) 5
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 11 (b) 12 (c) 13 (d) 5
  3. 3.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  4. 4.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 278 (b) 309 (c) 310 (d) 300
  5. 5.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) 27 (d) 9
  6. 6.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) 60 (d) 69
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 5 (b) 17 (c) 15 (d) 16
  8. 8.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 22 (c) 40 (d) 31
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 19 (b) 21 (c) 20 (d) 9
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 9 (d) 7
  11. 11.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  12. 12.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
  13. 13.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 343 (b) 300 (c) 333 (d) 342
  14. 14.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 91 (b) 82 (c) 92 (d) 100
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 21 (b) 20 (c) 19 (d) 9
  16. 16.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 98 (c) 80 (d) 90
  17. 17.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 77 (c) 68 (d) 78
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 53? (a) 16 (b) 14 (c) 15 (d) 5
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 2 (b) 1 (c) 4 (d) 3
  20. 20.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) 171 (b) 60 (c) 57 (d) 19
  21. 21.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  22. 22.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 34 (c) 44 (d) 43
  23. 23.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) 72 (d) 24
  24. 24.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) 39 (b) 42 (c) 13 (d) 117
  25. 25.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 160 (c) 169 (d) 178
  26. 26.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 14 (b) 4 (c) 16 (d) 15
  28. 28.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 93 (b) 102 (c) 94 (d) 84
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  30. 30.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 16 (b) 4 (c) 15 (d) 14
  32. 32.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 7 (d) 8
  33. 33.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  34. 34.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 488 (b) 615 (c) 624 (d) 625
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 14 (b) 15 (c) 3 (d) 13
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 18 (b) 6 (c) 17 (d) 16
  37. 37.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 8 (d) 10
  38. 38.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 42 (c) 14 (d) 45
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 3 (b) 2 (c) 1 (d) 4
  40. 40.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 326 (c) 381 (d) 372

Answer key

  1. 15
  2. 12
  3. 2
  4. 309
  5. 27
  6. 69
  7. 16
  8. 31
  9. 20
  10. 8
  11. 6
  12. 18
  13. 342
  14. 91
  15. 20
  16. 89
  17. 77
  18. 15
  19. 3
  20. 57
  21. 8
  22. 43
  23. 72
  24. 39
  25. 169
  26. 4
  27. 15
  28. 93
  29. 6
  30. 9
  31. 15
  32. 7
  33. 5
  34. 624
  35. 14
  36. 17
  37. 7
  38. 42
  39. 3
  40. 381

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