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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 216 · 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 6 written when you write all the numbers from 1 to 40? (a) 5 (b) 3 (c) 2 (d) 4
  2. 2.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) 30 (b) 90 (c) 33 (d) 10
  3. 3.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 360 (c) 370 (d) 318
  4. 4.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 161 (b) 152 (c) 162 (d) 170
  5. 5.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  6. 6.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 318 (c) 328 (d) 290
  7. 7.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 496 (c) 495 (d) 402
  8. 8.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 16 (b) 17 (c) 6 (d) 18
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 16 (b) 18 (c) 17 (d) 7
  11. 11.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) 9 (c) 30 (d) 81
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 8 (d) 10
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 18 (b) 8 (c) 20 (d) 19
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 3 (b) 1 (c) 2 (d) 4
  15. 15.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 426 (c) 532 (d) 531
  16. 16.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 75 (c) 66 (d) 76
  17. 17.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 300 (c) 343 (d) 333
  18. 18.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 262 (c) 285 (d) 276
  19. 19.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) 45 (c) 42 (d) 14
  20. 20.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) 7 (b) 21 (c) 24 (d) 63
  21. 21.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 171 (c) 162 (d) 172
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 18 (b) 8 (c) 17 (d) 19
  23. 23.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 350 (b) 418 (c) 408 (d) 417
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 6 (b) 17 (c) 16 (d) 18
  25. 25.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 118 (c) 110 (d) 109
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 7 (b) 19 (c) 17 (d) 18
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 18 (b) 16 (c) 17 (d) 6
  28. 28.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 177 (c) 168 (d) 178
  29. 29.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) 69 (b) 207 (c) 23 (d) 72
  30. 30.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 15 (b) 14 (c) 3 (d) 13
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 6 (b) 8 (c) 5 (d) 7
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 4 (b) 16 (c) 15 (d) 14
  34. 34.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
  35. 35.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 10 (b) 12 (c) 4 (d) 11
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 18 (b) 19 (c) 7 (d) 17
  38. 38.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 628 (b) 627 (c) 618 (d) 490
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 52? (a) 5 (b) 4 (c) 6 (d) 3
  40. 40.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 622 (c) 621 (d) 612

Answer key

  1. 4
  2. 30
  3. 369
  4. 161
  5. 8
  6. 327
  7. 495
  8. 4
  9. 17
  10. 17
  11. 27
  12. 9
  13. 19
  14. 3
  15. 531
  16. 75
  17. 342
  18. 285
  19. 42
  20. 21
  21. 171
  22. 18
  23. 417
  24. 17
  25. 109
  26. 18
  27. 17
  28. 177
  29. 69
  30. 6
  31. 14
  32. 7
  33. 15
  34. 2
  35. 9
  36. 11
  37. 18
  38. 627
  39. 5
  40. 621

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