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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 766 · 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 3? (a) 3 (b) 2 (c) 10 (d) 4
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  3. 3.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 5 (b) 2 (c) 3 (d) 4
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
  6. 6.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) 528 (c) 529 (d) 424
  7. 7.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 285 (c) 268 (d) 295
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 17 (b) 16 (c) 15 (d) 6
  9. 9.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 10 (d) 6
  10. 10.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) 475 (c) 465 (d) 474
  11. 11.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) 135 (c) 48 (d) 45
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 15 (b) 14 (c) 13 (d) 4
  13. 13.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) 33 (c) 30 (d) 10
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 18 (b) 16 (c) 6 (d) 17
  15. 15.The numbers 3 to 11 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) 63 (c) 7 (d) 21
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 18 (b) 17 (c) 16 (d) 7
  17. 17.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) 207 (b) 69 (c) 72 (d) 23
  18. 18.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) 117 (b) 13 (c) 42 (d) 39
  19. 19.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 78? (a) 19 (b) 7 (c) 18 (d) 17
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 12 (b) 14 (c) 3 (d) 13
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 18 (b) 17 (c) 19 (d) 7
  23. 23.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 86? (a) 8 (b) 18 (c) 20 (d) 19
  25. 25.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 2 (b) 5 (c) 4 (d) 3
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 44? (a) 4 (b) 2 (c) 5 (d) 3
  28. 28.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) 30 (b) 81 (c) 27 (d) 9
  29. 29.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) 18 (b) 57 (c) 54 (d) 162
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 15 (b) 5 (c) 16 (d) 17
  31. 31.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  32. 32.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  33. 33.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 625 (c) 615 (d) 488
  34. 34.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) 66 (c) 198 (d) 22
  35. 35.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 133 (b) 124 (c) 134 (d) 142
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 5 (b) 7 (c) 6 (d) 4
  37. 37.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
  38. 38.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 135 (c) 144 (d) 126
  39. 39.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) 430 (c) 429 (d) 358
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 3 (b) 15 (c) 14 (d) 13

Answer key

  1. 3
  2. 9
  3. 9
  4. 4
  5. 6
  6. 528
  7. 294
  8. 16
  9. 7
  10. 474
  11. 45
  12. 14
  13. 30
  14. 17
  15. 21
  16. 17
  17. 69
  18. 39
  19. 3
  20. 18
  21. 13
  22. 18
  23. 4
  24. 19
  25. 6
  26. 4
  27. 4
  28. 27
  29. 54
  30. 16
  31. 5
  32. 8
  33. 624
  34. 66
  35. 133
  36. 6
  37. 51
  38. 135
  39. 429
  40. 14

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