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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 91 · 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 two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  2. 2.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 505 (b) 495 (c) 504 (d) 408
  3. 3.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 180 (c) 188 (d) 179
  4. 4.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 469 (b) 459 (c) 468 (d) 384
  5. 5.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 78 (c) 88 (d) 87
  6. 6.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 6 (d) 14
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  8. 8.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 26 (c) 44 (d) 35
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 21 (b) 9 (c) 20 (d) 19
  10. 10.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) 21 (d) 63
  11. 11.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 32 (c) 41 (d) 42
  12. 12.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) 54 (c) 18 (d) 162
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 18 (d) 20
  14. 14.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) 27 (b) 81 (c) 30 (d) 9
  15. 15.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 549 (c) 438 (d) 550
  16. 16.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 392 (b) 471 (c) 481 (d) 480
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 7 (b) 4 (c) 6 (d) 5
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 20 (b) 8 (c) 19 (d) 18
  19. 19.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  20. 20.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  21. 21.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) 51 (c) 16 (d) 48
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 2 (b) 4 (c) 5 (d) 3
  23. 23.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) 153 (b) 54 (c) 51 (d) 17
  24. 24.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 104 (c) 86 (d) 95
  25. 25.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 488 (c) 624 (d) 625
  26. 26.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 101 (c) 92 (d) 102
  27. 27.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 1 (b) 2 (c) 4 (d) 3
  29. 29.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
  30. 30.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
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 4 (b) 1 (c) 3 (d) 2
  32. 32.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) 23 (b) 207 (c) 69 (d) 72
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 16 (b) 14 (c) 4 (d) 15
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 7 (b) 17 (c) 18 (d) 16
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 3 (d) 4
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 7 (b) 4 (c) 5 (d) 6
  37. 37.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 174 (c) 182 (d) 173
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 4 (b) 6 (c) 7 (d) 5
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 9 (b) 11 (c) 12 (d) 8
  40. 40.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 367 (c) 366 (d) 357

Answer key

  1. 9
  2. 504
  3. 179
  4. 468
  5. 87
  6. 6
  7. 6
  8. 35
  9. 20
  10. 63
  11. 41
  12. 54
  13. 19
  14. 27
  15. 549
  16. 480
  17. 6
  18. 19
  19. 4
  20. 9
  21. 48
  22. 4
  23. 51
  24. 95
  25. 624
  26. 101
  27. 5
  28. 3
  29. 18
  30. 72
  31. 3
  32. 69
  33. 15
  34. 17
  35. 3
  36. 6
  37. 173
  38. 6
  39. 11
  40. 366

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