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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 40 · 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) 9 (d) 11
  2. 2.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 445 (b) 368 (c) 444 (d) 435
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 3 (b) 4 (c) 5 (d) 2
  4. 4.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 100 (c) 92 (d) 91
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 19 (b) 9 (c) 18 (d) 20
  6. 6.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  7. 7.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 80 (c) 88 (d) 79
  8. 8.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 126 (c) 125 (d) 116
  9. 9.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 618 (c) 627 (d) 628
  10. 10.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 18 (b) 16 (c) 17 (d) 6
  12. 12.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 45 (b) 46 (c) 36 (d) 54
  13. 13.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 5 (b) 7 (c) 4 (d) 6
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 9 (b) 19 (c) 20 (d) 21
  16. 16.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) 39 (c) 13 (d) 42
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 16 (b) 4 (c) 15 (d) 14
  18. 18.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 351 (c) 306 (d) 342
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 18 (b) 20 (c) 9 (d) 19
  20. 20.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) 424 (c) 519 (d) 528
  21. 21.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  22. 22.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  23. 23.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 9 (b) 21 (c) 20 (d) 19
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 9 (b) 19 (c) 20 (d) 18
  26. 26.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) 108 (c) 36 (d) 12
  27. 27.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 15 (b) 14 (c) 3 (d) 13
  29. 29.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 394 (c) 483 (d) 474
  30. 30.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 358 (c) 429 (d) 420
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 16 (b) 17 (c) 5 (d) 15
  32. 32.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) 19 (c) 171 (d) 57
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 6 (b) 15 (c) 16 (d) 17
  34. 34.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) 51 (c) 144 (d) 48
  35. 35.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 471 (b) 386 (c) 462 (d) 472
  36. 36.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 87 (b) 78 (c) 88 (d) 96
  37. 37.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) 63 (b) 66 (c) 189 (d) 21
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 6 (b) 5 (c) 4 (d) 3
  39. 39.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
  40. 40.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) 5 (d) 18

Answer key

  1. 9
  2. 444
  3. 4
  4. 91
  5. 19
  6. 5
  7. 79
  8. 125
  9. 627
  10. 7
  11. 17
  12. 45
  13. 6
  14. 6
  15. 20
  16. 39
  17. 15
  18. 351
  19. 19
  20. 528
  21. 2
  22. 5
  23. 2
  24. 20
  25. 19
  26. 36
  27. 6
  28. 14
  29. 483
  30. 429
  31. 16
  32. 57
  33. 16
  34. 48
  35. 471
  36. 87
  37. 63
  38. 5
  39. 24
  40. 15

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