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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 706 · 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 7? (a) 6 (b) 7 (c) 10 (d) 8
  2. 2.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 214 (b) 204 (c) 321 (d) 213
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 14 (b) 16 (c) 15 (d) 5
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 14 (b) 16 (c) 15 (d) 4
  5. 5.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) 8 (b) 27 (c) 24 (d) 72
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 16 (b) 14 (c) 15 (d) 5
  7. 7.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 14 (b) 13 (c) 15 (d) 3
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 20 (b) 8 (c) 19 (d) 18
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 45? (a) 3 (b) 4 (c) 5 (d) 6
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 10 (b) 11 (c) 9 (d) 8
  12. 12.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  13. 13.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 101 (b) 102 (c) 92 (d) 110
  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) 11 (b) 33 (c) 99 (d) 36
  15. 15.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  17. 17.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 356 (b) 427 (c) 417 (d) 426
  18. 18.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) 30 (b) 33 (c) 90 (d) 10
  19. 19.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  20. 20.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  21. 21.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 28 (b) 46 (c) 38 (d) 37
  22. 22.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 309 (b) 319 (c) 318 (d) 284
  23. 23.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 290 (c) 328 (d) 327
  24. 24.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) 22 (b) 66 (c) 69 (d) 198
  25. 25.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4
  26. 26.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) 13 (b) 39 (c) 117 (d) 42
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 91? (a) 20 (b) 18 (c) 19 (d) 9
  28. 28.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) 180 (c) 60 (d) 63
  29. 29.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) 18 (b) 15 (c) 5 (d) 45
  30. 30.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 83 (b) 84 (c) 92 (d) 74
  31. 31.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 348 (c) 405 (d) 415
  32. 32.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) 72 (c) 69 (d) 23
  33. 33.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) 54 (c) 57 (d) 162
  34. 34.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 609 (c) 618 (d) 619
  35. 35.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  36. 36.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  37. 37.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) 48 (c) 144 (d) 51
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 20 (b) 19 (c) 21 (d) 9
  39. 39.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 400 (c) 493 (d) 492
  40. 40.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 5 (d) 15

Answer key

  1. 7
  2. 213
  3. 15
  4. 15
  5. 24
  6. 15
  7. 9
  8. 14
  9. 19
  10. 5
  11. 10
  12. 6
  13. 101
  14. 33
  15. 8
  16. 3
  17. 426
  18. 30
  19. 4
  20. 8
  21. 37
  22. 318
  23. 327
  24. 66
  25. 3
  26. 39
  27. 19
  28. 60
  29. 15
  30. 83
  31. 414
  32. 69
  33. 54
  34. 618
  35. 6
  36. 9
  37. 48
  38. 20
  39. 492
  40. 5

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