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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 36 · 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 6? (a) 10 (b) 7 (c) 6 (d) 5
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 16 (b) 14 (c) 5 (d) 15
  3. 3.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 169 (b) 170 (c) 160 (d) 178
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 57? (a) 6 (b) 4 (c) 3 (d) 5
  5. 5.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 17 (d) 3
  6. 6.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) 17 (b) 153 (c) 51 (d) 54
  7. 7.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 67 (c) 68 (d) 58
  8. 8.The numbers 18 to 26 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) 198 (c) 22 (d) 69
  9. 9.The numbers 16 to 24 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) 20 (c) 60 (d) 180
  10. 10.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 75 (b) 84 (c) 66 (d) 76
  11. 11.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 240 (c) 243 (d) 253
  12. 12.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 519 (b) 528 (c) 424 (d) 529
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3
  14. 14.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 111 (b) 120 (c) 102 (d) 112
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 8 (b) 18 (c) 19 (d) 20
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 3 (b) 14 (c) 13 (d) 12
  17. 17.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 156 (c) 165 (d) 174
  18. 18.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) 48 (b) 15 (c) 135 (d) 45
  19. 19.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) 72 (b) 216 (c) 75 (d) 24
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 3 (b) 4 (c) 1 (d) 2
  21. 21.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  22. 22.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 372 (c) 451 (d) 450
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 16 (b) 5 (c) 17 (d) 15
  24. 24.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 342 (c) 396 (d) 406
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 15 (b) 16 (c) 5 (d) 14
  26. 26.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 222 (c) 226 (d) 231
  27. 27.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 603 (c) 613 (d) 612
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 96? (a) 16 (b) 14 (c) 9 (d) 17
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 6 (b) 7 (c) 8 (d) 5
  30. 30.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 72 (c) 71 (d) 62
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 70? (a) 16 (b) 7 (c) 18 (d) 17
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 5 (b) 4 (c) 2 (d) 3
  33. 33.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 1 (d) 18
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 3 (b) 1 (c) 4 (d) 2
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 17 (b) 6 (c) 16 (d) 18
  36. 36.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 466 (c) 382 (d) 465
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 12 (b) 11 (c) 9 (d) 6
  38. 38.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
  39. 39.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  40. 40.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6

Answer key

  1. 6
  2. 15
  3. 169
  4. 5
  5. 3
  6. 51
  7. 67
  8. 66
  9. 60
  10. 75
  11. 252
  12. 528
  13. 4
  14. 111
  15. 19
  16. 13
  17. 165
  18. 45
  19. 72
  20. 3
  21. 9
  22. 450
  23. 16
  24. 405
  25. 15
  26. 231
  27. 612
  28. 16
  29. 7
  30. 71
  31. 17
  32. 4
  33. 2
  34. 3
  35. 17
  36. 465
  37. 11
  38. 8
  39. 2
  40. 7

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