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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 605 · 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.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 75 (b) 84 (c) 76 (d) 66
  2. 2.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  3. 3.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) 18 (b) 6 (c) 21 (d) 54
  4. 4.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 113 (c) 122 (d) 114
  5. 5.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 2 (b) 3 (c) 5 (d) 4
  7. 7.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 321 (c) 312 (d) 286
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 21 (b) 19 (c) 9 (d) 20
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  11. 11.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) 33 (b) 30 (c) 90 (d) 10
  12. 12.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
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  14. 14.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 9 (d) 10
  15. 15.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 85 (c) 94 (d) 76
  16. 16.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 372 (c) 450 (d) 451
  17. 17.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 213 (c) 223 (d) 222
  18. 18.The numbers 8 to 16 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) 108 (c) 12 (d) 36
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 18 (b) 20 (c) 19 (d) 8
  20. 20.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) 92 (c) 74 (d) 84
  21. 21.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 66 (c) 74 (d) 65
  22. 22.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
  23. 23.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  24. 24.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) 24 (c) 27 (d) 72
  25. 25.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) 5 (b) 15 (c) 45 (d) 18
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 6 (b) 7 (c) 5 (d) 8
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 88? (a) 20 (b) 19 (c) 8 (d) 18
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 19 (b) 18 (c) 8 (d) 20
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 17 (b) 8 (c) 18 (d) 19
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 5 (b) 6 (c) 7 (d) 8
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 4 (b) 14 (c) 16 (d) 15
  32. 32.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 274 (c) 304 (d) 294
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 9 (d) 20
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 17 (d) 19
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 17 (d) 8
  36. 36.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 7 (b) 24 (c) 21 (d) 63
  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) 144 (b) 48 (c) 16 (d) 51
  38. 38.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 640 (c) 498 (d) 639
  39. 39.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) 23 (b) 207 (c) 72 (d) 69
  40. 40.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 11 (d) 10

Answer key

  1. 75
  2. 3
  3. 18
  4. 113
  5. 9
  6. 4
  7. 321
  8. 5
  9. 20
  10. 8
  11. 30
  12. 33
  13. 4
  14. 8
  15. 85
  16. 450
  17. 222
  18. 36
  19. 19
  20. 83
  21. 65
  22. 5
  23. 3
  24. 24
  25. 15
  26. 7
  27. 19
  28. 19
  29. 18
  30. 7
  31. 15
  32. 303
  33. 20
  34. 18
  35. 18
  36. 21
  37. 48
  38. 639
  39. 69
  40. 9

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