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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 368 · 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 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 327 (c) 337 (d) 336
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 65? (a) 4 (b) 5 (c) 6 (d) 7
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 40? (a) 5 (b) 4 (c) 6 (d) 3
  4. 4.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 5 (b) 6 (c) 4 (d) 3
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 17 (b) 15 (c) 16 (d) 6
  7. 7.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 7 (d) 5
  8. 8.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 351 (c) 352 (d) 342
  9. 9.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4
  10. 10.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 21 (b) 19 (c) 20 (d) 9
  12. 12.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 223 (b) 220 (c) 222 (d) 213
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  14. 14.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 198 (c) 208 (d) 207
  15. 15.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 16 (b) 5 (c) 17 (d) 15
  17. 17.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 74 (c) 56 (d) 65
  18. 18.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) 171 (c) 57 (d) 19
  19. 19.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) 15 (c) 45 (d) 18
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 3 (b) 11 (c) 9 (d) 10
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 9 (b) 4 (c) 11 (d) 10
  22. 22.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) 45 (b) 15 (c) 135 (d) 48
  23. 23.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) 45 (b) 14 (c) 126 (d) 42
  24. 24.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 101 (c) 102 (d) 92
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 5 (b) 16 (c) 17 (d) 15
  26. 26.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 19 (b) 21 (c) 20 (d) 9
  28. 28.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) 18 (c) 57 (d) 54
  29. 29.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 454 (c) 453 (d) 374
  30. 30.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 67 (b) 68 (c) 58 (d) 76
  31. 31.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
  32. 32.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 3 (b) 15 (c) 14 (d) 13
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 7 (b) 6 (c) 5 (d) 4
  35. 35.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) 51 (c) 17 (d) 54
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 14 (b) 13 (c) 3 (d) 15
  37. 37.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) 192 (c) 174 (d) 184
  38. 38.The numbers 3 to 11 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) 63 (c) 7 (d) 21
  39. 39.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) 51 (b) 16 (c) 144 (d) 48
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 8 (b) 9 (c) 11 (d) 12

Answer key

  1. 336
  2. 6
  3. 5
  4. 5
  5. 5
  6. 16
  7. 6
  8. 351
  9. 3
  10. 3
  11. 20
  12. 222
  13. 4
  14. 207
  15. 7
  16. 16
  17. 65
  18. 57
  19. 15
  20. 10
  21. 10
  22. 45
  23. 42
  24. 101
  25. 16
  26. 4
  27. 20
  28. 54
  29. 453
  30. 67
  31. 6
  32. 2
  33. 14
  34. 6
  35. 51
  36. 14
  37. 183
  38. 21
  39. 48
  40. 11

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