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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 31 · 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 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 70 (c) 79 (d) 88
  2. 2.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 58? (a) 3 (b) 6 (c) 4 (d) 5
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 6 (b) 17 (c) 18 (d) 16
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 5 (b) 6 (c) 7 (d) 8
  6. 6.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 420 (c) 430 (d) 429
  7. 7.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4
  8. 8.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 92 (c) 101 (d) 110
  9. 9.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  10. 10.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) 5 (d) 45
  11. 11.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) 99 (c) 33 (d) 11
  12. 12.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) 228 (c) 224 (d) 219
  13. 13.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 508 (c) 507 (d) 410
  14. 14.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 19 (d) 17
  16. 16.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 130 (c) 148 (d) 139
  17. 17.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) 126 (b) 14 (c) 45 (d) 42
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 19 (b) 8 (c) 20 (d) 18
  19. 19.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  20. 20.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) 12 (b) 36 (c) 39 (d) 108
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 3 (b) 6 (c) 5 (d) 4
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 9 (b) 19 (c) 20 (d) 21
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 16 (b) 8 (c) 13 (d) 15
  24. 24.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 514 (b) 504 (c) 414 (d) 513
  25. 25.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) 135 (b) 15 (c) 48 (d) 45
  26. 26.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 184 (c) 183 (d) 192
  27. 27.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 8 (d) 10
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 4 (b) 1 (c) 2 (d) 3
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 14 (b) 16 (c) 5 (d) 15
  30. 30.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 261 (c) 271 (d) 252
  31. 31.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 568 (c) 567 (d) 558
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 2 (b) 3 (c) 4 (d) 1
  33. 33.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 9 (c) 30 (d) 27
  34. 34.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 20 (d) 19
  36. 36.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 243 (c) 253 (d) 252
  37. 37.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 415 (b) 348 (c) 405 (d) 414
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 4 (b) 16 (c) 14 (d) 15
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 6 (b) 16 (c) 17 (d) 18
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 19 (b) 18 (c) 7 (d) 17

Answer key

  1. 79
  2. 4
  3. 5
  4. 17
  5. 7
  6. 429
  7. 3
  8. 101
  9. 4
  10. 15
  11. 33
  12. 228
  13. 507
  14. 2
  15. 18
  16. 139
  17. 42
  18. 19
  19. 6
  20. 36
  21. 5
  22. 20
  23. 15
  24. 513
  25. 45
  26. 183
  27. 7
  28. 3
  29. 15
  30. 270
  31. 567
  32. 3
  33. 27
  34. 6
  35. 20
  36. 252
  37. 414
  38. 15
  39. 17
  40. 18

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