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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 191 · 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 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) 99 (b) 11 (c) 36 (d) 33
  2. 2.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) 23 (c) 72 (d) 69
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 68? (a) 4 (b) 7 (c) 5 (d) 6
  4. 4.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 643 (c) 500 (d) 642
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  6. 6.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 429 (c) 430 (d) 420
  7. 7.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
  8. 8.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 283 (b) 273 (c) 260 (d) 282
  9. 9.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) 45 (b) 135 (c) 48 (d) 15
  10. 10.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  11. 11.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  12. 12.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) 51 (b) 144 (c) 48 (d) 16
  13. 13.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) 22 (c) 66 (d) 69
  14. 14.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  15. 15.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) 10 (c) 90 (d) 33
  16. 16.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 51 (b) 60 (c) 42 (d) 52
  17. 17.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 122 (c) 121 (d) 130
  18. 18.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) 547 (c) 436 (d) 537
  19. 19.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
  20. 20.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 68 (c) 67 (d) 76
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 4 (b) 7 (c) 5 (d) 6
  22. 22.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) 5 (d) 45
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 3 (b) 12 (c) 14 (d) 13
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 15 (b) 14 (c) 13 (d) 3
  25. 25.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 402 (c) 403 (d) 340
  26. 26.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  27. 27.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  28. 28.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 358 (c) 357 (d) 348
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 15 (b) 17 (c) 6 (d) 16
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 20 (b) 19 (c) 9 (d) 18
  31. 31.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
  32. 32.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  33. 33.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) 63 (b) 20 (c) 60 (d) 180
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 5 (b) 3 (c) 4 (d) 2
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
  36. 36.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 540 (c) 541 (d) 531
  37. 37.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 63 (c) 189 (d) 66
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 17 (b) 19 (c) 18 (d) 7
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 20 (d) 9
  40. 40.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 282 (c) 266 (d) 292

Answer key

  1. 33
  2. 69
  3. 6
  4. 642
  5. 3
  6. 429
  7. 7
  8. 282
  9. 45
  10. 5
  11. 8
  12. 48
  13. 66
  14. 5
  15. 30
  16. 51
  17. 121
  18. 546
  19. 39
  20. 67
  21. 6
  22. 15
  23. 13
  24. 14
  25. 402
  26. 4
  27. 6
  28. 357
  29. 16
  30. 19
  31. 6
  32. 2
  33. 60
  34. 4
  35. 4
  36. 540
  37. 63
  38. 18
  39. 20
  40. 291

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