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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 652 · 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 9 written when you write all the numbers from 1 to 99? (a) 20 (b) 21 (c) 9 (d) 19
  2. 2.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) 72 (b) 8 (c) 24 (d) 27
  3. 3.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 445 (b) 368 (c) 444 (d) 435
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 4 (b) 6 (c) 3 (d) 5
  5. 5.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 158 (c) 148 (d) 157
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 18 (b) 19 (c) 20 (d) 8
  7. 7.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  8. 8.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) 207 (b) 72 (c) 69 (d) 23
  9. 9.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 45 (c) 54 (d) 46
  10. 10.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  11. 11.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) 21 (b) 7 (c) 63 (d) 24
  12. 12.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  13. 13.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) 189 (b) 21 (c) 63 (d) 66
  14. 14.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) 21 (b) 54 (c) 6 (d) 18
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 6 (b) 5 (c) 4 (d) 3
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 16 (b) 6 (c) 17 (d) 18
  17. 17.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 7 (b) 5 (c) 6 (d) 4
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 18 (d) 19
  20. 20.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) 60 (c) 20 (d) 180
  21. 21.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 574 (c) 564 (d) 573
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 15 (b) 4 (c) 14 (d) 16
  23. 23.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 277 (c) 267 (d) 276
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 17 (b) 6 (c) 18 (d) 16
  25. 25.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) 51 (b) 48 (c) 16 (d) 144
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 5 (b) 2 (c) 3 (d) 4
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 20 (b) 19 (c) 21 (d) 9
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 16 (b) 5 (c) 15 (d) 17
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 8 (b) 6 (c) 7 (d) 5
  30. 30.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 20 (b) 18 (c) 8 (d) 19
  32. 32.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) 36 (c) 99 (d) 33
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 7 (b) 16 (c) 17 (d) 18
  34. 34.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 286 (c) 285 (d) 276
  35. 35.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 229 (b) 224 (c) 228 (d) 219
  36. 36.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 110 (c) 100 (d) 109
  37. 37.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 20 (b) 19 (c) 18 (d) 9
  39. 39.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 380 (b) 453 (c) 462 (d) 463
  40. 40.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5

Answer key

  1. 20
  2. 24
  3. 444
  4. 5
  5. 157
  6. 19
  7. 4
  8. 69
  9. 45
  10. 5
  11. 21
  12. 8
  13. 63
  14. 18
  15. 5
  16. 17
  17. 3
  18. 6
  19. 18
  20. 60
  21. 573
  22. 15
  23. 276
  24. 17
  25. 48
  26. 4
  27. 20
  28. 16
  29. 7
  30. 2
  31. 19
  32. 33
  33. 17
  34. 285
  35. 228
  36. 109
  37. 5
  38. 19
  39. 462
  40. 4

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