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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 409 · 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 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 459 (b) 468 (c) 469 (d) 384
  2. 2.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 358 (c) 310 (d) 357
  3. 3.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) 45 (b) 126 (c) 14 (d) 42
  4. 4.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) 24 (b) 72 (c) 8 (d) 27
  5. 5.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) 18 (b) 57 (c) 54 (d) 162
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 5 (b) 3 (c) 4 (d) 2
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 9 (b) 6 (c) 8 (d) 7
  8. 8.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 78 (c) 69 (d) 70
  9. 9.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 48 (c) 47 (d) 56
  10. 10.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 42 (c) 51 (d) 60
  11. 11.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  12. 12.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 439 (c) 438 (d) 364
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 5 (d) 3
  14. 14.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) 42 (c) 39 (d) 13
  15. 15.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 187 (c) 178 (d) 188
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 94? (a) 15 (b) 9 (c) 14 (d) 12
  17. 17.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 372 (c) 451 (d) 441
  18. 18.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 15 (b) 14 (c) 16 (d) 4
  20. 20.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
  21. 21.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 128 (c) 118 (d) 127
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 4 (d) 3
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 14 (b) 16 (c) 15 (d) 4
  25. 25.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) 60 (b) 171 (c) 19 (d) 57
  26. 26.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  27. 27.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 142 (c) 151 (d) 160
  28. 28.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 480 (c) 398 (d) 490
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 4 (b) 14 (c) 16 (d) 15
  30. 30.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 155 (b) 164 (c) 146 (d) 156
  31. 31.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 3 (b) 2 (c) 4 (d) 5
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 20 (b) 19 (c) 21 (d) 9
  34. 34.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 177 (c) 186 (d) 178
  35. 35.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) 42 (c) 32 (d) 41
  36. 36.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 1 (d) 18
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 8 (b) 17 (c) 19 (d) 18
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 6 (b) 5 (c) 7 (d) 4
  39. 39.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 322 (c) 286 (d) 321
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 9 (b) 20 (c) 21 (d) 19

Answer key

  1. 468
  2. 357
  3. 42
  4. 24
  5. 54
  6. 4
  7. 8
  8. 69
  9. 47
  10. 51
  11. 9
  12. 438
  13. 4
  14. 39
  15. 187
  16. 14
  17. 450
  18. 9
  19. 15
  20. 15
  21. 127
  22. 3
  23. 3
  24. 15
  25. 57
  26. 6
  27. 151
  28. 489
  29. 15
  30. 155
  31. 5
  32. 4
  33. 20
  34. 177
  35. 41
  36. 2
  37. 18
  38. 6
  39. 321
  40. 20

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