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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 949 · 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 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) 57 (b) 171 (c) 19 (d) 60
  2. 2.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  3. 3.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 127 (b) 118 (c) 128 (d) 136
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 75? (a) 7 (b) 18 (c) 17 (d) 16
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  6. 6.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 8 (b) 6 (c) 5 (d) 7
  8. 8.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  9. 9.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) 16 (c) 144 (d) 48
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 9 (d) 7
  11. 11.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  12. 12.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) 72 (b) 216 (c) 75 (d) 24
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 4 (b) 14 (c) 15 (d) 16
  14. 14.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 113 (c) 122 (d) 104
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 3 (b) 2 (c) 5 (d) 4
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 17 (b) 19 (c) 7 (d) 18
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 82? (a) 6 (b) 9 (c) 7 (d) 8
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 5 (d) 16
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 8 (b) 7 (c) 6 (d) 9
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 5 (b) 4 (c) 2 (d) 3
  21. 21.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 379 (b) 324 (c) 369 (d) 378
  22. 22.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) 45 (b) 14 (c) 126 (d) 42
  23. 23.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 20 (b) 19 (c) 8 (d) 18
  25. 25.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 631 (c) 492 (d) 621
  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) 42 (b) 39 (c) 13 (d) 117
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 3 (b) 4 (c) 6 (d) 5
  28. 28.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) 72 (b) 69 (c) 23 (d) 207
  29. 29.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 34 (c) 33 (d) 42
  30. 30.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) 72 (d) 24
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 38? (a) 4 (b) 2 (c) 5 (d) 3
  32. 32.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 487 (b) 396 (c) 477 (d) 486
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 60? (a) 6 (b) 7 (c) 5 (d) 4
  34. 34.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 386 (b) 472 (c) 462 (d) 471
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 15 (b) 17 (c) 6 (d) 16
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 7 (b) 16 (c) 18 (d) 17
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 18 (d) 9
  38. 38.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
  39. 39.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) 99 (c) 36 (d) 33
  40. 40.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 337 (c) 336 (d) 327

Answer key

  1. 57
  2. 8
  3. 127
  4. 17
  5. 3
  6. 9
  7. 7
  8. 5
  9. 48
  10. 8
  11. 4
  12. 72
  13. 15
  14. 113
  15. 4
  16. 18
  17. 8
  18. 16
  19. 8
  20. 4
  21. 378
  22. 42
  23. 5
  24. 19
  25. 630
  26. 39
  27. 5
  28. 69
  29. 33
  30. 24
  31. 4
  32. 486
  33. 6
  34. 471
  35. 16
  36. 17
  37. 19
  38. 27
  39. 33
  40. 336

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