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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 357 · 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 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) 108 (c) 36 (d) 39
  2. 2.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 4 (b) 15 (c) 16 (d) 14
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 17 (b) 18 (c) 19 (d) 7
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 9 (b) 19 (c) 21 (d) 20
  6. 6.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) 19 (b) 60 (c) 171 (d) 57
  7. 7.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  8. 8.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) 66 (c) 69 (d) 22
  9. 9.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 291 (c) 266 (d) 292
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 3 (b) 4 (c) 5 (d) 2
  11. 11.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
  12. 12.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 400 (c) 399 (d) 338
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 12 (b) 13 (c) 11 (d) 3
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 18 (d) 7
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 6 (b) 8 (c) 9 (d) 7
  16. 16.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 180 (c) 172 (d) 171
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 77? (a) 6 (b) 5 (c) 7 (d) 8
  18. 18.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 168 (c) 160 (d) 159
  19. 19.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 19 (b) 7 (c) 17 (d) 18
  21. 21.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4
  22. 22.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 427 (c) 426 (d) 356
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 4 (b) 2 (c) 1 (d) 3
  24. 24.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 81 (b) 72 (c) 90 (d) 82
  25. 25.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) 63 (c) 60 (d) 180
  26. 26.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  27. 27.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) 48 (c) 135 (d) 45
  28. 28.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 17 (b) 15 (c) 5 (d) 16
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 19 (b) 18 (c) 20 (d) 8
  31. 31.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 586 (b) 576 (c) 585 (d) 462
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 5 (b) 8 (c) 6 (d) 7
  33. 33.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 86 (c) 94 (d) 85
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 88? (a) 20 (b) 8 (c) 18 (d) 19
  35. 35.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
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 6 (b) 16 (c) 17 (d) 18
  37. 37.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 436 (c) 547 (d) 537
  38. 38.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  39. 39.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 459 (c) 450 (d) 378
  40. 40.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) 40 (c) 22 (d) 31

Answer key

  1. 36
  2. 3
  3. 15
  4. 18
  5. 20
  6. 57
  7. 6
  8. 66
  9. 291
  10. 4
  11. 8
  12. 399
  13. 12
  14. 18
  15. 8
  16. 171
  17. 7
  18. 159
  19. 5
  20. 18
  21. 3
  22. 426
  23. 3
  24. 81
  25. 60
  26. 7
  27. 45
  28. 9
  29. 16
  30. 19
  31. 585
  32. 7
  33. 85
  34. 19
  35. 27
  36. 17
  37. 546
  38. 7
  39. 459
  40. 31

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