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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 154 · 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 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 54 (c) 72 (d) 63
  2. 2.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 6 (b) 4 (c) 3 (d) 5
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 85? (a) 18 (b) 20 (c) 8 (d) 19
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 19 (b) 20 (c) 21 (d) 9
  6. 6.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
  7. 7.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 446 (b) 552 (c) 561 (d) 562
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 54? (a) 6 (b) 4 (c) 3 (d) 5
  9. 9.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) 27 (d) 30
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 18 (b) 7 (c) 17 (d) 16
  11. 11.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 362 (c) 426 (d) 436
  12. 12.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 17 (d) 3
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 16 (b) 18 (c) 17 (d) 7
  14. 14.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 167 (b) 168 (c) 158 (d) 176
  15. 15.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) 21 (b) 66 (c) 63 (d) 189
  16. 16.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  17. 17.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 92? (a) 20 (b) 9 (c) 18 (d) 19
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 14 (b) 3 (c) 13 (d) 15
  20. 20.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) 75 (b) 72 (c) 216 (d) 24
  21. 21.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 19 (b) 20 (c) 9 (d) 21
  23. 23.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) 90 (d) 33
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 5 (b) 4 (c) 6 (d) 3
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 78? (a) 7 (b) 18 (c) 17 (d) 19
  26. 26.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) 54 (b) 51 (c) 153 (d) 17
  27. 27.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) 88 (c) 79 (d) 70
  28. 28.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 337 (b) 296 (c) 336 (d) 327
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 16 (b) 17 (c) 6 (d) 18
  30. 30.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
  31. 31.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  32. 32.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 496 (b) 486 (c) 495 (d) 402
  33. 33.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) 19 (c) 60 (d) 171
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 3 (b) 14 (c) 13 (d) 12
  35. 35.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) 174 (c) 183 (d) 184
  36. 36.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) 27 (b) 72 (c) 8 (d) 24
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 18 (b) 17 (c) 16 (d) 6
  38. 38.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  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) 16 (b) 144 (c) 51 (d) 48
  40. 40.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9

Answer key

  1. 63
  2. 3
  3. 5
  4. 19
  5. 20
  6. 171
  7. 561
  8. 5
  9. 27
  10. 17
  11. 435
  12. 3
  13. 17
  14. 167
  15. 63
  16. 2
  17. 5
  18. 19
  19. 14
  20. 72
  21. 4
  22. 20
  23. 30
  24. 5
  25. 18
  26. 51
  27. 79
  28. 336
  29. 17
  30. 9
  31. 6
  32. 495
  33. 57
  34. 13
  35. 183
  36. 24
  37. 17
  38. 4
  39. 48
  40. 8

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