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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 525 · 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 2 written when you write all the numbers from 1 to 32? (a) 15 (b) 13 (c) 3 (d) 14
  2. 2.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 11 (c) 33 (d) 36
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
  4. 4.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) 42 (b) 14 (c) 126 (d) 45
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  6. 6.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  7. 7.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  8. 8.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 266 (b) 292 (c) 291 (d) 282
  9. 9.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) 54 (c) 21 (d) 18
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 3 (b) 5 (c) 4 (d) 2
  11. 11.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 174 (c) 184 (d) 192
  12. 12.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 142 (c) 151 (d) 160
  13. 13.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) 69 (b) 198 (c) 22 (d) 66
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 3 (b) 2 (c) 5 (d) 4
  15. 15.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 202 (c) 201 (d) 206
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 3 (b) 14 (c) 15 (d) 13
  17. 17.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 15 (b) 13 (c) 14 (d) 4
  19. 19.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 113 (b) 122 (c) 114 (d) 104
  20. 20.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 368 (b) 435 (c) 444 (d) 445
  21. 21.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) 71 (c) 62 (d) 72
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 2 (b) 1 (c) 3 (d) 4
  23. 23.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  24. 24.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) 20 (b) 63 (c) 60 (d) 180
  25. 25.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 50 (c) 59 (d) 68
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 10 (b) 13 (c) 8 (d) 12
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 15 (b) 4 (c) 16 (d) 14
  28. 28.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 457 (b) 447 (c) 456 (d) 376
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 16 (b) 15 (c) 6 (d) 17
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 85? (a) 20 (b) 19 (c) 18 (d) 8
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 77? (a) 8 (b) 5 (c) 6 (d) 7
  32. 32.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  33. 33.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 7 (b) 19 (c) 17 (d) 18
  35. 35.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) 18 (b) 5 (c) 15 (d) 45
  36. 36.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  37. 37.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 200 (b) 193 (c) 192 (d) 183
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 15 (b) 16 (c) 14 (d) 4
  39. 39.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  40. 40.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9

Answer key

  1. 14
  2. 33
  3. 6
  4. 42
  5. 3
  6. 4
  7. 5
  8. 291
  9. 18
  10. 4
  11. 183
  12. 151
  13. 66
  14. 4
  15. 201
  16. 14
  17. 7
  18. 14
  19. 113
  20. 444
  21. 71
  22. 3
  23. 9
  24. 60
  25. 59
  26. 12
  27. 15
  28. 456
  29. 16
  30. 19
  31. 7
  32. 2
  33. 3
  34. 18
  35. 15
  36. 2
  37. 192
  38. 15
  39. 9
  40. 8

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