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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 819 · 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 times is the digit 3 written when you write all the numbers from 1 to 30? (a) 2 (b) 5 (c) 3 (d) 4
  2. 2.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) 18 (c) 45 (d) 5
  3. 3.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 45 (b) 36 (c) 46 (d) 54
  4. 4.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
  5. 5.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 315 (c) 306 (d) 316
  6. 6.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  7. 7.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 169 (c) 160 (d) 170
  8. 8.The numbers 16 to 24 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) 20 (c) 60 (d) 180
  9. 9.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 211 (b) 210 (c) 201 (d) 212
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 15 (b) 14 (c) 13 (d) 3
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 5 (b) 6 (c) 7 (d) 8
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 16 (b) 17 (c) 5 (d) 15
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 82? (a) 19 (b) 17 (c) 8 (d) 18
  15. 15.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) 291 (c) 282 (d) 266
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 6 (b) 4 (c) 3 (d) 5
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 17 (b) 16 (c) 7 (d) 18
  18. 18.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 58? (a) 17 (b) 15 (c) 16 (d) 5
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 8 (b) 19 (c) 18 (d) 17
  21. 21.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) 18 (c) 54 (d) 21
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 20 (b) 21 (c) 9 (d) 19
  24. 24.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 17 (b) 7 (c) 18 (d) 19
  26. 26.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) 126 (c) 14 (d) 42
  27. 27.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) 60 (b) 19 (c) 171 (d) 57
  28. 28.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) 24 (d) 75
  29. 29.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 319 (b) 284 (c) 309 (d) 318
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 2 (b) 3 (c) 1 (d) 4
  31. 31.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 114 (c) 123 (d) 132
  32. 32.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) 17 (b) 153 (c) 54 (d) 51
  33. 33.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 120 (c) 111 (d) 102
  34. 34.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) 36 (b) 11 (c) 99 (d) 33
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 21 (b) 19 (c) 9 (d) 20
  36. 36.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) 22 (c) 198 (d) 66
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 7 (b) 17 (c) 16 (d) 18
  38. 38.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 280 (c) 270 (d) 279
  39. 39.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) 48 (b) 144 (c) 51 (d) 16
  40. 40.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3

Answer key

  1. 4
  2. 15
  3. 45
  4. 6
  5. 315
  6. 3
  7. 169
  8. 60
  9. 210
  10. 14
  11. 7
  12. 4
  13. 16
  14. 18
  15. 291
  16. 5
  17. 17
  18. 5
  19. 16
  20. 18
  21. 18
  22. 19
  23. 20
  24. 7
  25. 18
  26. 42
  27. 57
  28. 72
  29. 318
  30. 3
  31. 123
  32. 51
  33. 111
  34. 33
  35. 20
  36. 66
  37. 17
  38. 279
  39. 48
  40. 2

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