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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 382 · 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 11? (a) 7 (b) 12 (c) 9 (d) 8
  2. 2.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) 15 (b) 45 (c) 48 (d) 135
  3. 3.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 116 (c) 115 (d) 106
  4. 4.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) 45 (b) 15 (c) 18 (d) 5
  5. 5.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) 54 (b) 6 (c) 21 (d) 18
  6. 6.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 326 (c) 372 (d) 381
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 19 (b) 9 (c) 18 (d) 20
  8. 8.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 331 (b) 321 (c) 292 (d) 330
  9. 9.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
  10. 10.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
  11. 11.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 484 (c) 609 (d) 619
  12. 12.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 254 (c) 273 (d) 264
  13. 13.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 52 (c) 43 (d) 34
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 13 (b) 4 (c) 14 (d) 12
  15. 15.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 397 (b) 396 (c) 387 (d) 336
  16. 16.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 308 (b) 354 (c) 355 (d) 345
  17. 17.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  18. 18.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) 612 (c) 621 (d) 622
  19. 19.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) 39 (b) 36 (c) 108 (d) 12
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 9 (b) 20 (c) 21 (d) 19
  21. 21.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 249 (c) 244 (d) 259
  22. 22.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
  23. 23.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
  24. 24.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) 72 (b) 24 (c) 8 (d) 27
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 7 (b) 5 (c) 6 (d) 4
  26. 26.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 5 (b) 16 (c) 15 (d) 17
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 5 (b) 3 (c) 4 (d) 2
  29. 29.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  30. 30.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 529 (b) 528 (c) 424 (d) 519
  31. 31.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
  32. 32.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 405 (c) 406 (d) 396
  33. 33.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 531 (c) 432 (d) 541
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 14 (b) 13 (c) 3 (d) 15
  35. 35.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 7 (d) 9
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 17 (b) 19 (c) 18 (d) 7
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 4 (b) 6 (c) 3 (d) 7
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 19 (b) 17 (c) 18 (d) 7
  39. 39.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 19 (d) 20

Answer key

  1. 8
  2. 45
  3. 115
  4. 15
  5. 18
  6. 381
  7. 19
  8. 330
  9. 2
  10. 5
  11. 618
  12. 273
  13. 43
  14. 13
  15. 396
  16. 354
  17. 3
  18. 621
  19. 36
  20. 20
  21. 258
  22. 3
  23. 6
  24. 24
  25. 6
  26. 9
  27. 16
  28. 4
  29. 6
  30. 528
  31. 7
  32. 405
  33. 540
  34. 14
  35. 8
  36. 18
  37. 6
  38. 18
  39. 9
  40. 19

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