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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 319 · 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 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 417 (c) 418 (d) 350
  2. 2.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 5 (b) 4 (c) 6 (d) 3
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 5 (b) 3 (c) 4 (d) 6
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 15 (b) 17 (c) 16 (d) 5
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 18 (b) 19 (c) 8 (d) 17
  9. 9.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
  10. 10.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) 75 (b) 24 (c) 216 (d) 72
  11. 11.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
  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) 54 (d) 36
  13. 13.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) 144 (b) 16 (c) 48 (d) 51
  14. 14.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 84 (c) 93 (d) 94
  15. 15.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) 5 (b) 45 (c) 18 (d) 15
  16. 16.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 81 (c) 82 (d) 90
  17. 17.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 380 (c) 463 (d) 462
  18. 18.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 436 (c) 537 (d) 547
  19. 19.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 600 (b) 601 (c) 472 (d) 591
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 17 (b) 18 (c) 19 (d) 7
  21. 21.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 441 (c) 442 (d) 366
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 5 (b) 8 (c) 6 (d) 7
  23. 23.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) 13 (b) 117 (c) 39 (d) 42
  24. 24.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) 51 (b) 54 (c) 17 (d) 153
  25. 25.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
  26. 26.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) 33 (b) 30 (c) 90 (d) 10
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 18 (b) 9 (c) 19 (d) 20
  28. 28.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) 6 (b) 18 (c) 21 (d) 54
  29. 29.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 5 (d) 15
  30. 30.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 5 (b) 3 (c) 4 (d) 2
  32. 32.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 134 (c) 125 (d) 126
  33. 33.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 9 (b) 21 (c) 19 (d) 20
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 15 (b) 13 (c) 4 (d) 14
  36. 36.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 9 (d) 10
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 15 (b) 4 (c) 16 (d) 14
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 1 (b) 4 (c) 2 (d) 3
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 5 (b) 6 (c) 8 (d) 7
  40. 40.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 107 (b) 98 (c) 116 (d) 108

Answer key

  1. 417
  2. 3
  3. 5
  4. 5
  5. 6
  6. 5
  7. 16
  8. 18
  9. 2
  10. 72
  11. 9
  12. 45
  13. 48
  14. 93
  15. 15
  16. 81
  17. 462
  18. 546
  19. 600
  20. 18
  21. 441
  22. 7
  23. 39
  24. 51
  25. 4
  26. 30
  27. 19
  28. 18
  29. 5
  30. 8
  31. 4
  32. 125
  33. 2
  34. 20
  35. 14
  36. 8
  37. 15
  38. 3
  39. 7
  40. 107

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