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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 878 · 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 72? (a) 16 (b) 17 (c) 7 (d) 18
  2. 2.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 429 (c) 439 (d) 438
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 8 (b) 18 (c) 20 (d) 19
  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) 11 (b) 99 (c) 33 (d) 36
  5. 5.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 201 (c) 211 (d) 212
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 80? (a) 8 (b) 17 (c) 18 (d) 19
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
  8. 8.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 418 (c) 520 (d) 519
  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) 15 (b) 45 (c) 18 (d) 5
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 90? (a) 9 (b) 19 (c) 20 (d) 18
  11. 11.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) 60 (c) 171 (d) 19
  12. 12.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  13. 13.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  14. 14.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 3 (b) 14 (c) 13 (d) 15
  16. 16.The numbers 14 to 22 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) 162 (c) 54 (d) 18
  17. 17.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 69 (b) 60 (c) 78 (d) 70
  18. 18.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  19. 19.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 149 (c) 158 (d) 140
  20. 20.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 9 (b) 21 (c) 20 (d) 19
  22. 22.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) 66 (b) 189 (c) 63 (d) 21
  23. 23.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 556 (b) 442 (c) 546 (d) 555
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 18 (b) 20 (c) 19 (d) 8
  25. 25.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) 117 (b) 39 (c) 42 (d) 13
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 20 (b) 18 (c) 19 (d) 8
  27. 27.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) 54 (b) 6 (c) 21 (d) 18
  28. 28.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
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 18 (b) 19 (c) 17 (d) 8
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 80? (a) 19 (b) 8 (c) 17 (d) 18
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 5 (b) 3 (c) 4 (d) 2
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 17 (b) 19 (c) 7 (d) 18
  33. 33.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) 48 (d) 15
  34. 34.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) 134 (d) 125
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 16 (b) 14 (c) 15 (d) 5
  36. 36.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 172 (c) 171 (d) 180
  37. 37.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 6 (b) 3 (c) 4 (d) 5
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 2 (b) 5 (c) 3 (d) 4
  40. 40.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) 20 (b) 63 (c) 180 (d) 60

Answer key

  1. 17
  2. 438
  3. 19
  4. 33
  5. 210
  6. 18
  7. 4
  8. 519
  9. 15
  10. 19
  11. 57
  12. 7
  13. 7
  14. 6
  15. 14
  16. 54
  17. 69
  18. 9
  19. 149
  20. 5
  21. 20
  22. 63
  23. 555
  24. 19
  25. 39
  26. 19
  27. 18
  28. 48
  29. 18
  30. 18
  31. 4
  32. 18
  33. 45
  34. 125
  35. 15
  36. 171
  37. 3
  38. 5
  39. 4
  40. 60

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