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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 300 · 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) 45 (c) 18 (d) 5
  2. 2.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) 153 (b) 51 (c) 17 (d) 54
  3. 3.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 225 (c) 216 (d) 226
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 14 (b) 16 (c) 15 (d) 4
  5. 5.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 18 (b) 20 (c) 19 (d) 9
  7. 7.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) 14 (b) 42 (c) 45 (d) 126
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 5 (b) 4 (c) 2 (d) 3
  9. 9.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  10. 10.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  11. 11.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  12. 12.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 609 (c) 478 (d) 600
  13. 13.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 298 (c) 297 (d) 288
  14. 14.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) 54 (c) 18 (d) 21
  15. 15.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) 13 (c) 117 (d) 42
  16. 16.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) 66 (b) 22 (c) 69 (d) 198
  17. 17.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 464 (b) 589 (c) 579 (d) 588
  18. 18.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) 27 (b) 8 (c) 24 (d) 72
  19. 19.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 163 (c) 164 (d) 172
  20. 20.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 12 (b) 13 (c) 10 (d) 8
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 14 (b) 13 (c) 15 (d) 3
  23. 23.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) 162 (c) 57 (d) 54
  24. 24.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 3 (d) 4
  26. 26.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
  27. 27.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 265 (c) 248 (d) 264
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 10 (b) 9 (c) 11 (d) 4
  29. 29.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 65 (b) 66 (c) 74 (d) 56
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 15 (b) 16 (c) 13 (d) 9
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 19 (b) 20 (c) 18 (d) 8
  32. 32.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 16 (b) 18 (c) 6 (d) 17
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 6 (b) 4 (c) 5 (d) 3
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 14 (b) 15 (c) 4 (d) 16
  36. 36.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) 372 (d) 381
  37. 37.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) 75 (b) 72 (c) 24 (d) 216
  38. 38.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 417 (c) 418 (d) 350
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 20 (b) 8 (c) 18 (d) 19
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 14 (b) 16 (c) 4 (d) 15

Answer key

  1. 15
  2. 51
  3. 225
  4. 15
  5. 8
  6. 19
  7. 42
  8. 4
  9. 9
  10. 4
  11. 7
  12. 609
  13. 297
  14. 18
  15. 39
  16. 66
  17. 588
  18. 24
  19. 163
  20. 9
  21. 12
  22. 14
  23. 54
  24. 4
  25. 4
  26. 2
  27. 264
  28. 10
  29. 65
  30. 15
  31. 19
  32. 2
  33. 17
  34. 5
  35. 15
  36. 381
  37. 72
  38. 417
  39. 19
  40. 15

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