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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 334 · 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 12? (a) 7 (b) 8 (c) 13 (d) 6
  2. 2.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  3. 3.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  4. 4.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 116 (c) 125 (d) 134
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 16 (b) 17 (c) 5 (d) 15
  6. 6.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 183 (c) 184 (d) 174
  7. 7.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
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 5 (b) 17 (c) 15 (d) 16
  9. 9.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10
  10. 10.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 266 (c) 282 (d) 291
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 54? (a) 5 (b) 15 (c) 17 (d) 16
  12. 12.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 150 (c) 158 (d) 149
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 1 (b) 4 (c) 2 (d) 3
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 5 (b) 3 (c) 2 (d) 4
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 5 (b) 8 (c) 7 (d) 6
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 14 (b) 13 (c) 12 (d) 3
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 18 (b) 20 (c) 8 (d) 19
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 6 (b) 10 (c) 9 (d) 7
  19. 19.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 496 (c) 402 (d) 495
  20. 20.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) 63 (b) 24 (c) 7 (d) 21
  21. 21.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 120 (c) 130 (d) 129
  22. 22.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 107 (c) 108 (d) 98
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 3 (b) 2 (c) 4 (d) 5
  24. 24.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) 63 (b) 189 (c) 21 (d) 66
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 19 (b) 9 (c) 21 (d) 20
  26. 26.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 16 (b) 6 (c) 17 (d) 18
  28. 28.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) 19 (b) 171 (c) 57 (d) 60
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 17 (b) 8 (c) 18 (d) 19
  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) 24 (d) 72
  31. 31.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) 15 (d) 48
  32. 32.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  33. 33.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 138 (c) 156 (d) 147
  34. 34.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 180 (c) 171 (d) 162
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 8 (b) 3 (c) 9 (d) 7
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 3 (b) 6 (c) 4 (d) 5
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 78? (a) 17 (b) 18 (c) 7 (d) 19
  38. 38.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
  39. 39.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) 108 (b) 36 (c) 39 (d) 12
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 4 (d) 3

Answer key

  1. 7
  2. 5
  3. 4
  4. 125
  5. 16
  6. 183
  7. 30
  8. 16
  9. 9
  10. 291
  11. 16
  12. 149
  13. 3
  14. 4
  15. 7
  16. 13
  17. 19
  18. 9
  19. 495
  20. 21
  21. 129
  22. 107
  23. 4
  24. 63
  25. 20
  26. 5
  27. 17
  28. 57
  29. 18
  30. 24
  31. 45
  32. 2
  33. 147
  34. 171
  35. 8
  36. 5
  37. 18
  38. 4
  39. 36
  40. 3

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