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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 240 · 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 1 written when you write all the numbers from 1 to 80? (a) 18 (b) 8 (c) 19 (d) 17
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 14 (b) 3 (c) 15 (d) 13
  3. 3.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 426 (c) 427 (d) 356
  4. 4.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) 153 (b) 17 (c) 51 (d) 54
  5. 5.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) 90 (b) 30 (c) 10 (d) 33
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 46? (a) 4 (b) 12 (c) 13 (d) 11
  7. 7.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 50 (c) 58 (d) 49
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 16 (b) 17 (c) 18 (d) 6
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 4 (b) 1 (c) 3 (d) 2
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
  11. 11.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 196 (c) 187 (d) 188
  12. 12.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
  13. 13.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 3 (b) 13 (c) 15 (d) 14
  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) 15 (b) 45 (c) 18 (d) 5
  16. 16.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) 12 (b) 39 (c) 36 (d) 108
  17. 17.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 265 (b) 264 (c) 248 (d) 255
  18. 18.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) 18 (b) 21 (c) 54 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 17 (b) 15 (c) 6 (d) 16
  21. 21.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) 216 (b) 75 (c) 72 (d) 24
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 7 (b) 18 (c) 16 (d) 17
  23. 23.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 501 (c) 511 (d) 412
  24. 24.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 96? (a) 9 (b) 19 (c) 20 (d) 21
  26. 26.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) 51 (c) 16 (d) 48
  27. 27.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 366 (c) 375 (d) 322
  28. 28.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 82 (c) 91 (d) 92
  29. 29.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) 126 (b) 42 (c) 14 (d) 45
  30. 30.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 162 (b) 57 (c) 54 (d) 18
  31. 31.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) 24 (b) 8 (c) 27 (d) 72
  32. 32.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 256 (c) 255 (d) 242
  33. 33.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 129 (b) 120 (c) 130 (d) 138
  34. 34.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 7 (b) 19 (c) 17 (d) 18
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 4 (b) 10 (c) 12 (d) 11
  37. 37.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 80 (c) 89 (d) 98
  38. 38.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 4 (b) 3 (c) 1 (d) 2
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 20 (d) 9

Answer key

  1. 18
  2. 14
  3. 426
  4. 51
  5. 30
  6. 12
  7. 49
  8. 17
  9. 3
  10. 3
  11. 187
  12. 7
  13. 4
  14. 14
  15. 15
  16. 36
  17. 264
  18. 18
  19. 9
  20. 16
  21. 72
  22. 17
  23. 510
  24. 5
  25. 20
  26. 48
  27. 375
  28. 91
  29. 42
  30. 54
  31. 24
  32. 255
  33. 129
  34. 9
  35. 18
  36. 11
  37. 89
  38. 4
  39. 3
  40. 20

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