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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 986 · 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 14? (a) 5 (b) 6 (c) 15 (d) 4
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 4 (b) 2 (c) 3 (d) 1
  3. 3.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) 19 (c) 60 (d) 171
  4. 4.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) 36 (c) 11 (d) 33
  5. 5.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  6. 6.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 16 (b) 17 (c) 18 (d) 7
  8. 8.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 434 (b) 544 (c) 534 (d) 543
  9. 9.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) 45 (b) 18 (c) 5 (d) 15
  10. 10.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 54 (c) 45 (d) 36
  11. 11.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) 198 (c) 66 (d) 22
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 17 (b) 18 (c) 16 (d) 6
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 16 (b) 15 (c) 5 (d) 14
  14. 14.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 262 (c) 276 (d) 285
  15. 15.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) 144 (b) 16 (c) 51 (d) 48
  16. 16.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) 24 (b) 72 (c) 27 (d) 8
  17. 17.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 318 (c) 369 (d) 370
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 4 (b) 3 (c) 2 (d) 5
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 5 (b) 6 (c) 7 (d) 4
  20. 20.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
  22. 22.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 88 (c) 87 (d) 78
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 43? (a) 2 (b) 3 (c) 4 (d) 5
  24. 24.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 562 (c) 446 (d) 552
  25. 25.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  26. 26.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 4 (d) 6
  27. 27.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 53 (b) 44 (c) 54 (d) 62
  28. 28.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 338 (b) 390 (c) 400 (d) 399
  29. 29.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 290 (b) 327 (c) 318 (d) 328
  30. 30.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  31. 31.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) 10 (b) 30 (c) 33 (d) 90
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 8 (b) 20 (c) 19 (d) 18
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 82? (a) 18 (b) 17 (c) 8 (d) 19
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 7 (b) 6 (c) 4 (d) 5
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 4 (b) 15 (c) 14 (d) 13
  36. 36.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) 48 (b) 135 (c) 45 (d) 15
  37. 37.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 3 (b) 14 (c) 15 (d) 13
  39. 39.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) 122 (c) 104 (d) 113
  40. 40.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) 42 (b) 126 (c) 45 (d) 14

Answer key

  1. 5
  2. 3
  3. 57
  4. 33
  5. 9
  6. 7
  7. 17
  8. 543
  9. 15
  10. 45
  11. 66
  12. 17
  13. 15
  14. 285
  15. 48
  16. 24
  17. 369
  18. 4
  19. 6
  20. 6
  21. 7
  22. 87
  23. 4
  24. 561
  25. 8
  26. 5
  27. 53
  28. 399
  29. 327
  30. 4
  31. 30
  32. 19
  33. 18
  34. 6
  35. 14
  36. 45
  37. 9
  38. 14
  39. 113
  40. 42

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